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Metamath Proof Explorer |
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| Ref | Description |
| idi 1 | (_Note_: This inference r... |
| a1ii 2 | (_Note_: This inference r... |
| mp2 9 | A double modus ponens infe... |
| mp2b 10 | A double modus ponens infe... |
| a1i 11 | Inference introducing an a... |
| 2a1i 12 | Inference introducing two ... |
| mp1i 13 | Inference detaching an ant... |
| a2i 14 | Inference distributing an ... |
| mpd 15 | A modus ponens deduction. ... |
| imim2i 16 | Inference adding common an... |
| syl 17 | An inference version of th... |
| 3syl 18 | Inference chaining two syl... |
| 4syl 19 | Inference chaining three s... |
| mpi 20 | A nested modus ponens infe... |
| mpisyl 21 | A syllogism combined with ... |
| id 22 | Principle of identity. Th... |
| idALT 23 | Alternate proof of ~ id . ... |
| idd 24 | Principle of identity ~ id... |
| a1d 25 | Deduction introducing an e... |
| 2a1d 26 | Deduction introducing two ... |
| a1i13 27 | Add two antecedents to a w... |
| 2a1 28 | A double form of ~ ax-1 . ... |
| a2d 29 | Deduction distributing an ... |
| sylcom 30 | Syllogism inference with c... |
| syl5com 31 | Syllogism inference with c... |
| com12 32 | Inference that swaps (comm... |
| syl11 33 | A syllogism inference. Co... |
| syl5 34 | A syllogism rule of infere... |
| syl6 35 | A syllogism rule of infere... |
| syl56 36 | Combine ~ syl5 and ~ syl6 ... |
| syl6com 37 | Syllogism inference with c... |
| mpcom 38 | Modus ponens inference wit... |
| syli 39 | Syllogism inference with c... |
| syl2im 40 | Replace two antecedents. ... |
| syl2imc 41 | A commuted version of ~ sy... |
| pm2.27 42 | This theorem, sometimes ca... |
| mpdd 43 | A nested modus ponens dedu... |
| mpid 44 | A nested modus ponens dedu... |
| mpdi 45 | A nested modus ponens dedu... |
| mpii 46 | A doubly nested modus pone... |
| syld 47 | Syllogism deduction. Dedu... |
| syldc 48 | Syllogism deduction. Comm... |
| mp2d 49 | A double modus ponens dedu... |
| a1dd 50 | Double deduction introduci... |
| 2a1dd 51 | Double deduction introduci... |
| pm2.43i 52 | Inference absorbing redund... |
| pm2.43d 53 | Deduction absorbing redund... |
| pm2.43a 54 | Inference absorbing redund... |
| pm2.43b 55 | Inference absorbing redund... |
| pm2.43 56 | Absorption of redundant an... |
| imim2d 57 | Deduction adding nested an... |
| imim2 58 | A closed form of syllogism... |
| embantd 59 | Deduction embedding an ant... |
| 3syld 60 | Triple syllogism deduction... |
| sylsyld 61 | A double syllogism inferen... |
| imim12i 62 | Inference joining two impl... |
| imim1i 63 | Inference adding common co... |
| imim3i 64 | Inference adding three nes... |
| sylc 65 | A syllogism inference comb... |
| syl3c 66 | A syllogism inference comb... |
| syl6mpi 67 | A syllogism inference. (C... |
| mpsyl 68 | Modus ponens combined with... |
| mpsylsyld 69 | Modus ponens combined with... |
| syl6c 70 | Inference combining ~ syl6... |
| syl6ci 71 | A syllogism inference comb... |
| syldd 72 | Nested syllogism deduction... |
| syl5d 73 | A nested syllogism deducti... |
| syl7 74 | A syllogism rule of infere... |
| syl6d 75 | A nested syllogism deducti... |
| syl8 76 | A syllogism rule of infere... |
| syl9 77 | A nested syllogism inferen... |
| syl9r 78 | A nested syllogism inferen... |
| syl10 79 | A nested syllogism inferen... |
| a1ddd 80 | Triple deduction introduci... |
| imim12d 81 | Deduction combining antece... |
| imim1d 82 | Deduction adding nested co... |
| imim1 83 | A closed form of syllogism... |
| pm2.83 84 | Theorem *2.83 of [Whitehea... |
| peirceroll 85 | Over minimal implicational... |
| com23 86 | Commutation of antecedents... |
| com3r 87 | Commutation of antecedents... |
| com13 88 | Commutation of antecedents... |
| com3l 89 | Commutation of antecedents... |
| pm2.04 90 | Swap antecedents. Theorem... |
| com34 91 | Commutation of antecedents... |
| com4l 92 | Commutation of antecedents... |
| com4t 93 | Commutation of antecedents... |
| com4r 94 | Commutation of antecedents... |
| com24 95 | Commutation of antecedents... |
| com14 96 | Commutation of antecedents... |
| com45 97 | Commutation of antecedents... |
| com35 98 | Commutation of antecedents... |
| com25 99 | Commutation of antecedents... |
| com5l 100 | Commutation of antecedents... |
| com15 101 | Commutation of antecedents... |
| com52l 102 | Commutation of antecedents... |
| com52r 103 | Commutation of antecedents... |
| com5r 104 | Commutation of antecedents... |
| imim12 105 | Closed form of ~ imim12i a... |
| jarr 106 | Elimination of a nested an... |
| jarri 107 | Inference associated with ... |
| pm2.86d 108 | Deduction associated with ... |
| pm2.86 109 | Converse of Axiom ~ ax-2 .... |
| pm2.86i 110 | Inference associated with ... |
| loolin 111 | The Linearity Axiom of the... |
| loowoz 112 | An alternate for the Linea... |
| con4 113 | Alias for ~ ax-3 to be use... |
| con4i 114 | Inference associated with ... |
| con4d 115 | Deduction associated with ... |
| mt4 116 | The rule of modus tollens.... |
| mt4d 117 | Modus tollens deduction. ... |
| mt4i 118 | Modus tollens inference. ... |
| pm2.21i 119 | A contradiction implies an... |
| pm2.24ii 120 | A contradiction implies an... |
| pm2.21d 121 | A contradiction implies an... |
| pm2.21ddALT 122 | Alternate proof of ~ pm2.2... |
| pm2.21 123 | From a wff and its negatio... |
| pm2.24 124 | Theorem *2.24 of [Whitehea... |
| jarl 125 | Elimination of a nested an... |
| jarli 126 | Inference associated with ... |
| pm2.18d 127 | Deduction form of the Clav... |
| pm2.18 128 | Clavius law, or "consequen... |
| pm2.18OLD 129 | Obsolete version of ~ pm2.... |
| pm2.18dOLD 130 | Obsolete version of ~ pm2.... |
| pm2.18i 131 | Inference associated with ... |
| notnotr 132 | Double negation eliminatio... |
| notnotri 133 | Inference associated with ... |
| notnotriALT 134 | Alternate proof of ~ notno... |
| notnotrd 135 | Deduction associated with ... |
| con2d 136 | A contraposition deduction... |
| con2 137 | Contraposition. Theorem *... |
| mt2d 138 | Modus tollens deduction. ... |
| mt2i 139 | Modus tollens inference. ... |
| nsyl3 140 | A negated syllogism infere... |
| con2i 141 | A contraposition inference... |
| nsyl 142 | A negated syllogism infere... |
| nsyl2 143 | A negated syllogism infere... |
| notnot 144 | Double negation introducti... |
| notnoti 145 | Inference associated with ... |
| notnotd 146 | Deduction associated with ... |
| con1d 147 | A contraposition deduction... |
| con1 148 | Contraposition. Theorem *... |
| con1i 149 | A contraposition inference... |
| mt3d 150 | Modus tollens deduction. ... |
| mt3i 151 | Modus tollens inference. ... |
| nsyl2OLD 152 | Obsolete version of ~ nsyl... |
| pm2.24i 153 | Inference associated with ... |
| pm2.24d 154 | Deduction form of ~ pm2.24... |
| con3d 155 | A contraposition deduction... |
| con3 156 | Contraposition. Theorem *... |
| con3i 157 | A contraposition inference... |
| con3rr3 158 | Rotate through consequent ... |
| nsyld 159 | A negated syllogism deduct... |
| nsyli 160 | A negated syllogism infere... |
| nsyl4 161 | A negated syllogism infere... |
| nsyl5 162 | A negated syllogism infere... |
| pm3.2im 163 | Theorem *3.2 of [Whitehead... |
| jc 164 | Deduction joining the cons... |
| jcn 165 | Theorem joining the conseq... |
| jcnd 166 | Deduction joining the cons... |
| impi 167 | An importation inference. ... |
| expi 168 | An exportation inference. ... |
| simprim 169 | Simplification. Similar t... |
| simplim 170 | Simplification. Similar t... |
| pm2.5g 171 | General instance of Theore... |
| pm2.5 172 | Theorem *2.5 of [Whitehead... |
| conax1 173 | Contrapositive of ~ ax-1 .... |
| conax1k 174 | Weakening of ~ conax1 . G... |
| pm2.51 175 | Theorem *2.51 of [Whitehea... |
| pm2.52 176 | Theorem *2.52 of [Whitehea... |
| pm2.521g 177 | A general instance of Theo... |
| pm2.521g2 178 | A general instance of Theo... |
| pm2.521 179 | Theorem *2.521 of [Whitehe... |
| expt 180 | Exportation theorem ~ pm3.... |
| impt 181 | Importation theorem ~ pm3.... |
| pm2.61d 182 | Deduction eliminating an a... |
| pm2.61d1 183 | Inference eliminating an a... |
| pm2.61d2 184 | Inference eliminating an a... |
| pm2.61i 185 | Inference eliminating an a... |
| pm2.61ii 186 | Inference eliminating two ... |
| pm2.61nii 187 | Inference eliminating two ... |
| pm2.61iii 188 | Inference eliminating thre... |
| ja 189 | Inference joining the ante... |
| jad 190 | Deduction form of ~ ja . ... |
| pm2.61iOLD 191 | Obsolete version of ~ pm2.... |
| pm2.01 192 | Weak Clavius law. If a fo... |
| pm2.01d 193 | Deduction based on reducti... |
| pm2.6 194 | Theorem *2.6 of [Whitehead... |
| pm2.61 195 | Theorem *2.61 of [Whitehea... |
| pm2.65 196 | Theorem *2.65 of [Whitehea... |
| pm2.65i 197 | Inference for proof by con... |
| pm2.21dd 198 | A contradiction implies an... |
| pm2.65d 199 | Deduction for proof by con... |
| mto 200 | The rule of modus tollens.... |
| mtod 201 | Modus tollens deduction. ... |
| mtoi 202 | Modus tollens inference. ... |
| mt2 203 | A rule similar to modus to... |
| mt3 204 | A rule similar to modus to... |
| peirce 205 | Peirce's axiom. A non-int... |
| looinv 206 | The Inversion Axiom of the... |
| bijust0 207 | A self-implication (see ~ ... |
| bijust 208 | Theorem used to justify th... |
| impbi 211 | Property of the biconditio... |
| impbii 212 | Infer an equivalence from ... |
| impbidd 213 | Deduce an equivalence from... |
| impbid21d 214 | Deduce an equivalence from... |
| impbid 215 | Deduce an equivalence from... |
| dfbi1 216 | Relate the biconditional c... |
| dfbi1ALT 217 | Alternate proof of ~ dfbi1... |
| biimp 218 | Property of the biconditio... |
| biimpi 219 | Infer an implication from ... |
| sylbi 220 | A mixed syllogism inferenc... |
| sylib 221 | A mixed syllogism inferenc... |
| sylbb 222 | A mixed syllogism inferenc... |
| biimpr 223 | Property of the biconditio... |
| bicom1 224 | Commutative law for the bi... |
| bicom 225 | Commutative law for the bi... |
| bicomd 226 | Commute two sides of a bic... |
| bicomi 227 | Inference from commutative... |
| impbid1 228 | Infer an equivalence from ... |
| impbid2 229 | Infer an equivalence from ... |
| impcon4bid 230 | A variation on ~ impbid wi... |
| biimpri 231 | Infer a converse implicati... |
| biimpd 232 | Deduce an implication from... |
| mpbi 233 | An inference from a bicond... |
| mpbir 234 | An inference from a bicond... |
| mpbid 235 | A deduction from a bicondi... |
| mpbii 236 | An inference from a nested... |
| sylibr 237 | A mixed syllogism inferenc... |
| sylbir 238 | A mixed syllogism inferenc... |
| sylbbr 239 | A mixed syllogism inferenc... |
| sylbb1 240 | A mixed syllogism inferenc... |
| sylbb2 241 | A mixed syllogism inferenc... |
| sylibd 242 | A syllogism deduction. (C... |
| sylbid 243 | A syllogism deduction. (C... |
| mpbidi 244 | A deduction from a bicondi... |
| syl5bi 245 | A mixed syllogism inferenc... |
| syl5bir 246 | A mixed syllogism inferenc... |
| syl5ib 247 | A mixed syllogism inferenc... |
| syl5ibcom 248 | A mixed syllogism inferenc... |
| syl5ibr 249 | A mixed syllogism inferenc... |
| syl5ibrcom 250 | A mixed syllogism inferenc... |
| biimprd 251 | Deduce a converse implicat... |
| biimpcd 252 | Deduce a commuted implicat... |
| biimprcd 253 | Deduce a converse commuted... |
| syl6ib 254 | A mixed syllogism inferenc... |
| syl6ibr 255 | A mixed syllogism inferenc... |
| syl6bi 256 | A mixed syllogism inferenc... |
| syl6bir 257 | A mixed syllogism inferenc... |
| syl7bi 258 | A mixed syllogism inferenc... |
| syl8ib 259 | A syllogism rule of infere... |
| mpbird 260 | A deduction from a bicondi... |
| mpbiri 261 | An inference from a nested... |
| sylibrd 262 | A syllogism deduction. (C... |
| sylbird 263 | A syllogism deduction. (C... |
| biid 264 | Principle of identity for ... |
| biidd 265 | Principle of identity with... |
| pm5.1im 266 | Two propositions are equiv... |
| 2th 267 | Two truths are equivalent.... |
| 2thd 268 | Two truths are equivalent.... |
| monothetic 269 | Two self-implications (see... |
| ibi 270 | Inference that converts a ... |
| ibir 271 | Inference that converts a ... |
| ibd 272 | Deduction that converts a ... |
| pm5.74 273 | Distribution of implicatio... |
| pm5.74i 274 | Distribution of implicatio... |
| pm5.74ri 275 | Distribution of implicatio... |
| pm5.74d 276 | Distribution of implicatio... |
| pm5.74rd 277 | Distribution of implicatio... |
| bitri 278 | An inference from transiti... |
| bitr2i 279 | An inference from transiti... |
| bitr3i 280 | An inference from transiti... |
| bitr4i 281 | An inference from transiti... |
| bitrd 282 | Deduction form of ~ bitri ... |
| bitr2d 283 | Deduction form of ~ bitr2i... |
| bitr3d 284 | Deduction form of ~ bitr3i... |
| bitr4d 285 | Deduction form of ~ bitr4i... |
| syl5bb 286 | A syllogism inference from... |
| syl5rbb 287 | A syllogism inference from... |
| bitr3id 288 | A syllogism inference from... |
| bitr3di 289 | A syllogism inference from... |
| bitrdi 290 | A syllogism inference from... |
| bitr2di 291 | A syllogism inference from... |
| bitr4di 292 | A syllogism inference from... |
| bitr4id 293 | A syllogism inference from... |
| 3imtr3i 294 | A mixed syllogism inferenc... |
| 3imtr4i 295 | A mixed syllogism inferenc... |
| 3imtr3d 296 | More general version of ~ ... |
| 3imtr4d 297 | More general version of ~ ... |
| 3imtr3g 298 | More general version of ~ ... |
| 3imtr4g 299 | More general version of ~ ... |
| 3bitri 300 | A chained inference from t... |
| 3bitrri 301 | A chained inference from t... |
| 3bitr2i 302 | A chained inference from t... |
| 3bitr2ri 303 | A chained inference from t... |
| 3bitr3i 304 | A chained inference from t... |
| 3bitr3ri 305 | A chained inference from t... |
| 3bitr4i 306 | A chained inference from t... |
| 3bitr4ri 307 | A chained inference from t... |
| 3bitrd 308 | Deduction from transitivit... |
| 3bitrrd 309 | Deduction from transitivit... |
| 3bitr2d 310 | Deduction from transitivit... |
| 3bitr2rd 311 | Deduction from transitivit... |
| 3bitr3d 312 | Deduction from transitivit... |
| 3bitr3rd 313 | Deduction from transitivit... |
| 3bitr4d 314 | Deduction from transitivit... |
| 3bitr4rd 315 | Deduction from transitivit... |
| 3bitr3g 316 | More general version of ~ ... |
| 3bitr4g 317 | More general version of ~ ... |
| notnotb 318 | Double negation. Theorem ... |
| con34b 319 | A biconditional form of co... |
| con4bid 320 | A contraposition deduction... |
| notbid 321 | Deduction negating both si... |
| notbi 322 | Contraposition. Theorem *... |
| notbii 323 | Negate both sides of a log... |
| con4bii 324 | A contraposition inference... |
| mtbi 325 | An inference from a bicond... |
| mtbir 326 | An inference from a bicond... |
| mtbid 327 | A deduction from a bicondi... |
| mtbird 328 | A deduction from a bicondi... |
| mtbii 329 | An inference from a bicond... |
| mtbiri 330 | An inference from a bicond... |
| sylnib 331 | A mixed syllogism inferenc... |
| sylnibr 332 | A mixed syllogism inferenc... |
| sylnbi 333 | A mixed syllogism inferenc... |
| sylnbir 334 | A mixed syllogism inferenc... |
| xchnxbi 335 | Replacement of a subexpres... |
| xchnxbir 336 | Replacement of a subexpres... |
| xchbinx 337 | Replacement of a subexpres... |
| xchbinxr 338 | Replacement of a subexpres... |
| imbi2i 339 | Introduce an antecedent to... |
| jcndOLD 340 | Obsolete version of ~ jcnd... |
| bibi2i 341 | Inference adding a bicondi... |
| bibi1i 342 | Inference adding a bicondi... |
| bibi12i 343 | The equivalence of two equ... |
| imbi2d 344 | Deduction adding an antece... |
| imbi1d 345 | Deduction adding a consequ... |
| bibi2d 346 | Deduction adding a bicondi... |
| bibi1d 347 | Deduction adding a bicondi... |
| imbi12d 348 | Deduction joining two equi... |
| bibi12d 349 | Deduction joining two equi... |
| imbi12 350 | Closed form of ~ imbi12i .... |
| imbi1 351 | Theorem *4.84 of [Whitehea... |
| imbi2 352 | Theorem *4.85 of [Whitehea... |
| imbi1i 353 | Introduce a consequent to ... |
| imbi12i 354 | Join two logical equivalen... |
| bibi1 355 | Theorem *4.86 of [Whitehea... |
| bitr3 356 | Closed nested implication ... |
| con2bi 357 | Contraposition. Theorem *... |
| con2bid 358 | A contraposition deduction... |
| con1bid 359 | A contraposition deduction... |
| con1bii 360 | A contraposition inference... |
| con2bii 361 | A contraposition inference... |
| con1b 362 | Contraposition. Bidirecti... |
| con2b 363 | Contraposition. Bidirecti... |
| biimt 364 | A wff is equivalent to its... |
| pm5.5 365 | Theorem *5.5 of [Whitehead... |
| a1bi 366 | Inference introducing a th... |
| mt2bi 367 | A false consequent falsifi... |
| mtt 368 | Modus-tollens-like theorem... |
| imnot 369 | If a proposition is false,... |
| pm5.501 370 | Theorem *5.501 of [Whitehe... |
| ibib 371 | Implication in terms of im... |
| ibibr 372 | Implication in terms of im... |
| tbt 373 | A wff is equivalent to its... |
| nbn2 374 | The negation of a wff is e... |
| bibif 375 | Transfer negation via an e... |
| nbn 376 | The negation of a wff is e... |
| nbn3 377 | Transfer falsehood via equ... |
| pm5.21im 378 | Two propositions are equiv... |
| 2false 379 | Two falsehoods are equival... |
| 2falsed 380 | Two falsehoods are equival... |
| 2falsedOLD 381 | Obsolete version of ~ 2fal... |
| pm5.21ni 382 | Two propositions implying ... |
| pm5.21nii 383 | Eliminate an antecedent im... |
| pm5.21ndd 384 | Eliminate an antecedent im... |
| bija 385 | Combine antecedents into a... |
| pm5.18 386 | Theorem *5.18 of [Whitehea... |
| xor3 387 | Two ways to express "exclu... |
| nbbn 388 | Move negation outside of b... |
| biass 389 | Associative law for the bi... |
| biluk 390 | Lukasiewicz's shortest axi... |
| pm5.19 391 | Theorem *5.19 of [Whitehea... |
| bi2.04 392 | Logical equivalence of com... |
| pm5.4 393 | Antecedent absorption impl... |
| imdi 394 | Distributive law for impli... |
| pm5.41 395 | Theorem *5.41 of [Whitehea... |
| pm4.8 396 | Theorem *4.8 of [Whitehead... |
| pm4.81 397 | A formula is equivalent to... |
| imim21b 398 | Simplify an implication be... |
| pm4.63 401 | Theorem *4.63 of [Whitehea... |
| pm4.67 402 | Theorem *4.67 of [Whitehea... |
| imnan 403 | Express an implication in ... |
| imnani 404 | Infer an implication from ... |
| iman 405 | Implication in terms of co... |
| pm3.24 406 | Law of noncontradiction. ... |
| annim 407 | Express a conjunction in t... |
| pm4.61 408 | Theorem *4.61 of [Whitehea... |
| pm4.65 409 | Theorem *4.65 of [Whitehea... |
| imp 410 | Importation inference. (C... |
| impcom 411 | Importation inference with... |
| con3dimp 412 | Variant of ~ con3d with im... |
| mpnanrd 413 | Eliminate the right side o... |
| impd 414 | Importation deduction. (C... |
| impcomd 415 | Importation deduction with... |
| ex 416 | Exportation inference. (T... |
| expcom 417 | Exportation inference with... |
| expdcom 418 | Commuted form of ~ expd . ... |
| expd 419 | Exportation deduction. (C... |
| expcomd 420 | Deduction form of ~ expcom... |
| imp31 421 | An importation inference. ... |
| imp32 422 | An importation inference. ... |
| exp31 423 | An exportation inference. ... |
| exp32 424 | An exportation inference. ... |
| imp4b 425 | An importation inference. ... |
| imp4a 426 | An importation inference. ... |
| imp4c 427 | An importation inference. ... |
| imp4d 428 | An importation inference. ... |
| imp41 429 | An importation inference. ... |
| imp42 430 | An importation inference. ... |
| imp43 431 | An importation inference. ... |
| imp44 432 | An importation inference. ... |
| imp45 433 | An importation inference. ... |
| exp4b 434 | An exportation inference. ... |
| exp4a 435 | An exportation inference. ... |
| exp4c 436 | An exportation inference. ... |
| exp4d 437 | An exportation inference. ... |
| exp41 438 | An exportation inference. ... |
| exp42 439 | An exportation inference. ... |
| exp43 440 | An exportation inference. ... |
| exp44 441 | An exportation inference. ... |
| exp45 442 | An exportation inference. ... |
| imp5d 443 | An importation inference. ... |
| imp5a 444 | An importation inference. ... |
| imp5g 445 | An importation inference. ... |
| imp55 446 | An importation inference. ... |
| imp511 447 | An importation inference. ... |
| exp5c 448 | An exportation inference. ... |
| exp5j 449 | An exportation inference. ... |
| exp5l 450 | An exportation inference. ... |
| exp53 451 | An exportation inference. ... |
| pm3.3 452 | Theorem *3.3 (Exp) of [Whi... |
| pm3.31 453 | Theorem *3.31 (Imp) of [Wh... |
| impexp 454 | Import-export theorem. Pa... |
| impancom 455 | Mixed importation/commutat... |
| expdimp 456 | A deduction version of exp... |
| expimpd 457 | Exportation followed by a ... |
| impr 458 | Import a wff into a right ... |
| impl 459 | Export a wff from a left c... |
| expr 460 | Export a wff from a right ... |
| expl 461 | Export a wff from a left c... |
| ancoms 462 | Inference commuting conjun... |
| pm3.22 463 | Theorem *3.22 of [Whitehea... |
| ancom 464 | Commutative law for conjun... |
| ancomd 465 | Commutation of conjuncts i... |
| biancomi 466 | Commuting conjunction in a... |
| biancomd 467 | Commuting conjunction in a... |
| ancomst 468 | Closed form of ~ ancoms . ... |
| ancomsd 469 | Deduction commuting conjun... |
| anasss 470 | Associative law for conjun... |
| anassrs 471 | Associative law for conjun... |
| anass 472 | Associative law for conjun... |
| pm3.2 473 | Join antecedents with conj... |
| pm3.2i 474 | Infer conjunction of premi... |
| pm3.21 475 | Join antecedents with conj... |
| pm3.43i 476 | Nested conjunction of ante... |
| pm3.43 477 | Theorem *3.43 (Comp) of [W... |
| dfbi2 478 | A theorem similar to the s... |
| dfbi 479 | Definition ~ df-bi rewritt... |
| biimpa 480 | Importation inference from... |
| biimpar 481 | Importation inference from... |
| biimpac 482 | Importation inference from... |
| biimparc 483 | Importation inference from... |
| adantr 484 | Inference adding a conjunc... |
| adantl 485 | Inference adding a conjunc... |
| simpl 486 | Elimination of a conjunct.... |
| simpli 487 | Inference eliminating a co... |
| simpr 488 | Elimination of a conjunct.... |
| simpri 489 | Inference eliminating a co... |
| intnan 490 | Introduction of conjunct i... |
| intnanr 491 | Introduction of conjunct i... |
| intnand 492 | Introduction of conjunct i... |
| intnanrd 493 | Introduction of conjunct i... |
| adantld 494 | Deduction adding a conjunc... |
| adantrd 495 | Deduction adding a conjunc... |
| pm3.41 496 | Theorem *3.41 of [Whitehea... |
| pm3.42 497 | Theorem *3.42 of [Whitehea... |
| simpld 498 | Deduction eliminating a co... |
| simprd 499 | Deduction eliminating a co... |
| simprbi 500 | Deduction eliminating a co... |
| simplbi 501 | Deduction eliminating a co... |
| simprbda 502 | Deduction eliminating a co... |
| simplbda 503 | Deduction eliminating a co... |
| simplbi2 504 | Deduction eliminating a co... |
| simplbi2comt 505 | Closed form of ~ simplbi2c... |
| simplbi2com 506 | A deduction eliminating a ... |
| simpl2im 507 | Implication from an elimin... |
| simplbiim 508 | Implication from an elimin... |
| impel 509 | An inference for implicati... |
| mpan9 510 | Modus ponens conjoining di... |
| sylan9 511 | Nested syllogism inference... |
| sylan9r 512 | Nested syllogism inference... |
| sylan9bb 513 | Nested syllogism inference... |
| sylan9bbr 514 | Nested syllogism inference... |
| jca 515 | Deduce conjunction of the ... |
| jcad 516 | Deduction conjoining the c... |
| jca2 517 | Inference conjoining the c... |
| jca31 518 | Join three consequents. (... |
| jca32 519 | Join three consequents. (... |
| jcai 520 | Deduction replacing implic... |
| jcab 521 | Distributive law for impli... |
| pm4.76 522 | Theorem *4.76 of [Whitehea... |
| jctil 523 | Inference conjoining a the... |
| jctir 524 | Inference conjoining a the... |
| jccir 525 | Inference conjoining a con... |
| jccil 526 | Inference conjoining a con... |
| jctl 527 | Inference conjoining a the... |
| jctr 528 | Inference conjoining a the... |
| jctild 529 | Deduction conjoining a the... |
| jctird 530 | Deduction conjoining a the... |
| iba 531 | Introduction of antecedent... |
| ibar 532 | Introduction of antecedent... |
| biantru 533 | A wff is equivalent to its... |
| biantrur 534 | A wff is equivalent to its... |
| biantrud 535 | A wff is equivalent to its... |
| biantrurd 536 | A wff is equivalent to its... |
| bianfi 537 | A wff conjoined with false... |
| bianfd 538 | A wff conjoined with false... |
| baib 539 | Move conjunction outside o... |
| baibr 540 | Move conjunction outside o... |
| rbaibr 541 | Move conjunction outside o... |
| rbaib 542 | Move conjunction outside o... |
| baibd 543 | Move conjunction outside o... |
| rbaibd 544 | Move conjunction outside o... |
| bianabs 545 | Absorb a hypothesis into t... |
| pm5.44 546 | Theorem *5.44 of [Whitehea... |
| pm5.42 547 | Theorem *5.42 of [Whitehea... |
| ancl 548 | Conjoin antecedent to left... |
| anclb 549 | Conjoin antecedent to left... |
| ancr 550 | Conjoin antecedent to righ... |
| ancrb 551 | Conjoin antecedent to righ... |
| ancli 552 | Deduction conjoining antec... |
| ancri 553 | Deduction conjoining antec... |
| ancld 554 | Deduction conjoining antec... |
| ancrd 555 | Deduction conjoining antec... |
| impac 556 | Importation with conjuncti... |
| anc2l 557 | Conjoin antecedent to left... |
| anc2r 558 | Conjoin antecedent to righ... |
| anc2li 559 | Deduction conjoining antec... |
| anc2ri 560 | Deduction conjoining antec... |
| pm4.71 561 | Implication in terms of bi... |
| pm4.71r 562 | Implication in terms of bi... |
| pm4.71i 563 | Inference converting an im... |
| pm4.71ri 564 | Inference converting an im... |
| pm4.71d 565 | Deduction converting an im... |
| pm4.71rd 566 | Deduction converting an im... |
| pm4.24 567 | Theorem *4.24 of [Whitehea... |
| anidm 568 | Idempotent law for conjunc... |
| anidmdbi 569 | Conjunction idempotence wi... |
| anidms 570 | Inference from idempotent ... |
| imdistan 571 | Distribution of implicatio... |
| imdistani 572 | Distribution of implicatio... |
| imdistanri 573 | Distribution of implicatio... |
| imdistand 574 | Distribution of implicatio... |
| imdistanda 575 | Distribution of implicatio... |
| pm5.3 576 | Theorem *5.3 of [Whitehead... |
| pm5.32 577 | Distribution of implicatio... |
| pm5.32i 578 | Distribution of implicatio... |
| pm5.32ri 579 | Distribution of implicatio... |
| pm5.32d 580 | Distribution of implicatio... |
| pm5.32rd 581 | Distribution of implicatio... |
| pm5.32da 582 | Distribution of implicatio... |
| sylan 583 | A syllogism inference. (C... |
| sylanb 584 | A syllogism inference. (C... |
| sylanbr 585 | A syllogism inference. (C... |
| sylanbrc 586 | Syllogism inference. (Con... |
| syl2anc 587 | Syllogism inference combin... |
| syl2anc2 588 | Double syllogism inference... |
| sylancl 589 | Syllogism inference combin... |
| sylancr 590 | Syllogism inference combin... |
| sylancom 591 | Syllogism inference with c... |
| sylanblc 592 | Syllogism inference combin... |
| sylanblrc 593 | Syllogism inference combin... |
| syldan 594 | A syllogism deduction with... |
| sylbida 595 | A syllogism deduction. (C... |
| sylan2 596 | A syllogism inference. (C... |
| sylan2b 597 | A syllogism inference. (C... |
| sylan2br 598 | A syllogism inference. (C... |
| syl2an 599 | A double syllogism inferen... |
| syl2anr 600 | A double syllogism inferen... |
| syl2anb 601 | A double syllogism inferen... |
| syl2anbr 602 | A double syllogism inferen... |
| sylancb 603 | A syllogism inference comb... |
| sylancbr 604 | A syllogism inference comb... |
| syldanl 605 | A syllogism deduction with... |
| syland 606 | A syllogism deduction. (C... |
| sylani 607 | A syllogism inference. (C... |
| sylan2d 608 | A syllogism deduction. (C... |
| sylan2i 609 | A syllogism inference. (C... |
| syl2ani 610 | A syllogism inference. (C... |
| syl2and 611 | A syllogism deduction. (C... |
| anim12d 612 | Conjoin antecedents and co... |
| anim12d1 613 | Variant of ~ anim12d where... |
| anim1d 614 | Add a conjunct to right of... |
| anim2d 615 | Add a conjunct to left of ... |
| anim12i 616 | Conjoin antecedents and co... |
| anim12ci 617 | Variant of ~ anim12i with ... |
| anim1i 618 | Introduce conjunct to both... |
| anim1ci 619 | Introduce conjunct to both... |
| anim2i 620 | Introduce conjunct to both... |
| anim12ii 621 | Conjoin antecedents and co... |
| anim12dan 622 | Conjoin antecedents and co... |
| im2anan9 623 | Deduction joining nested i... |
| im2anan9r 624 | Deduction joining nested i... |
| pm3.45 625 | Theorem *3.45 (Fact) of [W... |
| anbi2i 626 | Introduce a left conjunct ... |
| anbi1i 627 | Introduce a right conjunct... |
| anbi2ci 628 | Variant of ~ anbi2i with c... |
| anbi1ci 629 | Variant of ~ anbi1i with c... |
| anbi12i 630 | Conjoin both sides of two ... |
| anbi12ci 631 | Variant of ~ anbi12i with ... |
| anbi2d 632 | Deduction adding a left co... |
| anbi1d 633 | Deduction adding a right c... |
| anbi12d 634 | Deduction joining two equi... |
| anbi1 635 | Introduce a right conjunct... |
| anbi2 636 | Introduce a left conjunct ... |
| anbi1cd 637 | Introduce a proposition as... |
| pm4.38 638 | Theorem *4.38 of [Whitehea... |
| bi2anan9 639 | Deduction joining two equi... |
| bi2anan9r 640 | Deduction joining two equi... |
| bi2bian9 641 | Deduction joining two bico... |
| bianass 642 | An inference to merge two ... |
| bianassc 643 | An inference to merge two ... |
| an21 644 | Swap two conjuncts. (Cont... |
| an12 645 | Swap two conjuncts. Note ... |
| an32 646 | A rearrangement of conjunc... |
| an13 647 | A rearrangement of conjunc... |
| an31 648 | A rearrangement of conjunc... |
| an12s 649 | Swap two conjuncts in ante... |
| ancom2s 650 | Inference commuting a nest... |
| an13s 651 | Swap two conjuncts in ante... |
| an32s 652 | Swap two conjuncts in ante... |
| ancom1s 653 | Inference commuting a nest... |
| an31s 654 | Swap two conjuncts in ante... |
| anass1rs 655 | Commutative-associative la... |
| an4 656 | Rearrangement of 4 conjunc... |
| an42 657 | Rearrangement of 4 conjunc... |
| an43 658 | Rearrangement of 4 conjunc... |
| an3 659 | A rearrangement of conjunc... |
| an4s 660 | Inference rearranging 4 co... |
| an42s 661 | Inference rearranging 4 co... |
| anabs1 662 | Absorption into embedded c... |
| anabs5 663 | Absorption into embedded c... |
| anabs7 664 | Absorption into embedded c... |
| anabsan 665 | Absorption of antecedent w... |
| anabss1 666 | Absorption of antecedent i... |
| anabss4 667 | Absorption of antecedent i... |
| anabss5 668 | Absorption of antecedent i... |
| anabsi5 669 | Absorption of antecedent i... |
| anabsi6 670 | Absorption of antecedent i... |
| anabsi7 671 | Absorption of antecedent i... |
| anabsi8 672 | Absorption of antecedent i... |
| anabss7 673 | Absorption of antecedent i... |
| anabsan2 674 | Absorption of antecedent w... |
| anabss3 675 | Absorption of antecedent i... |
| anandi 676 | Distribution of conjunctio... |
| anandir 677 | Distribution of conjunctio... |
| anandis 678 | Inference that undistribut... |
| anandirs 679 | Inference that undistribut... |
| sylanl1 680 | A syllogism inference. (C... |
| sylanl2 681 | A syllogism inference. (C... |
| sylanr1 682 | A syllogism inference. (C... |
| sylanr2 683 | A syllogism inference. (C... |
| syl6an 684 | A syllogism deduction comb... |
| syl2an2r 685 | ~ syl2anr with antecedents... |
| syl2an2 686 | ~ syl2an with antecedents ... |
| mpdan 687 | An inference based on modu... |
| mpancom 688 | An inference based on modu... |
| mpidan 689 | A deduction which "stacks"... |
| mpan 690 | An inference based on modu... |
| mpan2 691 | An inference based on modu... |
| mp2an 692 | An inference based on modu... |
| mp4an 693 | An inference based on modu... |
| mpan2d 694 | A deduction based on modus... |
| mpand 695 | A deduction based on modus... |
| mpani 696 | An inference based on modu... |
| mpan2i 697 | An inference based on modu... |
| mp2ani 698 | An inference based on modu... |
| mp2and 699 | A deduction based on modus... |
| mpanl1 700 | An inference based on modu... |
| mpanl2 701 | An inference based on modu... |
| mpanl12 702 | An inference based on modu... |
| mpanr1 703 | An inference based on modu... |
| mpanr2 704 | An inference based on modu... |
| mpanr12 705 | An inference based on modu... |
| mpanlr1 706 | An inference based on modu... |
| mpbirand 707 | Detach truth from conjunct... |
| mpbiran2d 708 | Detach truth from conjunct... |
| mpbiran 709 | Detach truth from conjunct... |
| mpbiran2 710 | Detach truth from conjunct... |
| mpbir2an 711 | Detach a conjunction of tr... |
| mpbi2and 712 | Detach a conjunction of tr... |
| mpbir2and 713 | Detach a conjunction of tr... |
| adantll 714 | Deduction adding a conjunc... |
| adantlr 715 | Deduction adding a conjunc... |
| adantrl 716 | Deduction adding a conjunc... |
| adantrr 717 | Deduction adding a conjunc... |
| adantlll 718 | Deduction adding a conjunc... |
| adantllr 719 | Deduction adding a conjunc... |
| adantlrl 720 | Deduction adding a conjunc... |
| adantlrr 721 | Deduction adding a conjunc... |
| adantrll 722 | Deduction adding a conjunc... |
| adantrlr 723 | Deduction adding a conjunc... |
| adantrrl 724 | Deduction adding a conjunc... |
| adantrrr 725 | Deduction adding a conjunc... |
| ad2antrr 726 | Deduction adding two conju... |
| ad2antlr 727 | Deduction adding two conju... |
| ad2antrl 728 | Deduction adding two conju... |
| ad2antll 729 | Deduction adding conjuncts... |
| ad3antrrr 730 | Deduction adding three con... |
| ad3antlr 731 | Deduction adding three con... |
| ad4antr 732 | Deduction adding 4 conjunc... |
| ad4antlr 733 | Deduction adding 4 conjunc... |
| ad5antr 734 | Deduction adding 5 conjunc... |
| ad5antlr 735 | Deduction adding 5 conjunc... |
| ad6antr 736 | Deduction adding 6 conjunc... |
| ad6antlr 737 | Deduction adding 6 conjunc... |
| ad7antr 738 | Deduction adding 7 conjunc... |
| ad7antlr 739 | Deduction adding 7 conjunc... |
| ad8antr 740 | Deduction adding 8 conjunc... |
| ad8antlr 741 | Deduction adding 8 conjunc... |
| ad9antr 742 | Deduction adding 9 conjunc... |
| ad9antlr 743 | Deduction adding 9 conjunc... |
| ad10antr 744 | Deduction adding 10 conjun... |
| ad10antlr 745 | Deduction adding 10 conjun... |
| ad2ant2l 746 | Deduction adding two conju... |
| ad2ant2r 747 | Deduction adding two conju... |
| ad2ant2lr 748 | Deduction adding two conju... |
| ad2ant2rl 749 | Deduction adding two conju... |
| adantl3r 750 | Deduction adding 1 conjunc... |
| ad4ant13 751 | Deduction adding conjuncts... |
| ad4ant14 752 | Deduction adding conjuncts... |
| ad4ant23 753 | Deduction adding conjuncts... |
| ad4ant24 754 | Deduction adding conjuncts... |
| adantl4r 755 | Deduction adding 1 conjunc... |
| ad5ant12 756 | Deduction adding conjuncts... |
| ad5ant13 757 | Deduction adding conjuncts... |
| ad5ant14 758 | Deduction adding conjuncts... |
| ad5ant15 759 | Deduction adding conjuncts... |
| ad5ant23 760 | Deduction adding conjuncts... |
| ad5ant24 761 | Deduction adding conjuncts... |
| ad5ant25 762 | Deduction adding conjuncts... |
| adantl5r 763 | Deduction adding 1 conjunc... |
| adantl6r 764 | Deduction adding 1 conjunc... |
| pm3.33 765 | Theorem *3.33 (Syll) of [W... |
| pm3.34 766 | Theorem *3.34 (Syll) of [W... |
| simpll 767 | Simplification of a conjun... |
| simplld 768 | Deduction form of ~ simpll... |
| simplr 769 | Simplification of a conjun... |
| simplrd 770 | Deduction eliminating a do... |
| simprl 771 | Simplification of a conjun... |
| simprld 772 | Deduction eliminating a do... |
| simprr 773 | Simplification of a conjun... |
| simprrd 774 | Deduction form of ~ simprr... |
| simplll 775 | Simplification of a conjun... |
| simpllr 776 | Simplification of a conjun... |
| simplrl 777 | Simplification of a conjun... |
| simplrr 778 | Simplification of a conjun... |
| simprll 779 | Simplification of a conjun... |
| simprlr 780 | Simplification of a conjun... |
| simprrl 781 | Simplification of a conjun... |
| simprrr 782 | Simplification of a conjun... |
| simp-4l 783 | Simplification of a conjun... |
| simp-4r 784 | Simplification of a conjun... |
| simp-5l 785 | Simplification of a conjun... |
| simp-5r 786 | Simplification of a conjun... |
| simp-6l 787 | Simplification of a conjun... |
| simp-6r 788 | Simplification of a conjun... |
| simp-7l 789 | Simplification of a conjun... |
| simp-7r 790 | Simplification of a conjun... |
| simp-8l 791 | Simplification of a conjun... |
| simp-8r 792 | Simplification of a conjun... |
| simp-9l 793 | Simplification of a conjun... |
| simp-9r 794 | Simplification of a conjun... |
| simp-10l 795 | Simplification of a conjun... |
| simp-10r 796 | Simplification of a conjun... |
| simp-11l 797 | Simplification of a conjun... |
| simp-11r 798 | Simplification of a conjun... |
| pm2.01da 799 | Deduction based on reducti... |
| pm2.18da 800 | Deduction based on reducti... |
| impbida 801 | Deduce an equivalence from... |
| pm5.21nd 802 | Eliminate an antecedent im... |
| pm3.35 803 | Conjunctive detachment. T... |
| pm5.74da 804 | Distribution of implicatio... |
| bitr 805 | Theorem *4.22 of [Whitehea... |
| biantr 806 | A transitive law of equiva... |
| pm4.14 807 | Theorem *4.14 of [Whitehea... |
| pm3.37 808 | Theorem *3.37 (Transp) of ... |
| anim12 809 | Conjoin antecedents and co... |
| pm3.4 810 | Conjunction implies implic... |
| exbiri 811 | Inference form of ~ exbir ... |
| pm2.61ian 812 | Elimination of an antecede... |
| pm2.61dan 813 | Elimination of an antecede... |
| pm2.61ddan 814 | Elimination of two anteced... |
| pm2.61dda 815 | Elimination of two anteced... |
| mtand 816 | A modus tollens deduction.... |
| pm2.65da 817 | Deduction for proof by con... |
| condan 818 | Proof by contradiction. (... |
| biadan 819 | An implication is equivale... |
| biadani 820 | Inference associated with ... |
| biadaniALT 821 | Alternate proof of ~ biada... |
| biadanii 822 | Inference associated with ... |
| pm5.1 823 | Two propositions are equiv... |
| pm5.21 824 | Two propositions are equiv... |
| pm5.35 825 | Theorem *5.35 of [Whitehea... |
| abai 826 | Introduce one conjunct as ... |
| pm4.45im 827 | Conjunction with implicati... |
| impimprbi 828 | An implication and its rev... |
| nan 829 | Theorem to move a conjunct... |
| pm5.31 830 | Theorem *5.31 of [Whitehea... |
| pm5.31r 831 | Variant of ~ pm5.31 . (Co... |
| pm4.15 832 | Theorem *4.15 of [Whitehea... |
| pm5.36 833 | Theorem *5.36 of [Whitehea... |
| annotanannot 834 | A conjunction with a negat... |
| pm5.33 835 | Theorem *5.33 of [Whitehea... |
| syl12anc 836 | Syllogism combined with co... |
| syl21anc 837 | Syllogism combined with co... |
| syl22anc 838 | Syllogism combined with co... |
| syl1111anc 839 | Four-hypothesis eliminatio... |
| syldbl2 840 | Stacked hypotheseis implie... |
| mpsyl4anc 841 | An elimination deduction. ... |
| pm4.87 842 | Theorem *4.87 of [Whitehea... |
| bimsc1 843 | Removal of conjunct from o... |
| a2and 844 | Deduction distributing a c... |
| animpimp2impd 845 | Deduction deriving nested ... |
| pm4.64 848 | Theorem *4.64 of [Whitehea... |
| pm4.66 849 | Theorem *4.66 of [Whitehea... |
| pm2.53 850 | Theorem *2.53 of [Whitehea... |
| pm2.54 851 | Theorem *2.54 of [Whitehea... |
| imor 852 | Implication in terms of di... |
| imori 853 | Infer disjunction from imp... |
| imorri 854 | Infer implication from dis... |
| pm4.62 855 | Theorem *4.62 of [Whitehea... |
| jaoi 856 | Inference disjoining the a... |
| jao1i 857 | Add a disjunct in the ante... |
| jaod 858 | Deduction disjoining the a... |
| mpjaod 859 | Eliminate a disjunction in... |
| ori 860 | Infer implication from dis... |
| orri 861 | Infer disjunction from imp... |
| orrd 862 | Deduce disjunction from im... |
| ord 863 | Deduce implication from di... |
| orci 864 | Deduction introducing a di... |
| olci 865 | Deduction introducing a di... |
| orc 866 | Introduction of a disjunct... |
| olc 867 | Introduction of a disjunct... |
| pm1.4 868 | Axiom *1.4 of [WhiteheadRu... |
| orcom 869 | Commutative law for disjun... |
| orcomd 870 | Commutation of disjuncts i... |
| orcoms 871 | Commutation of disjuncts i... |
| orcd 872 | Deduction introducing a di... |
| olcd 873 | Deduction introducing a di... |
| orcs 874 | Deduction eliminating disj... |
| olcs 875 | Deduction eliminating disj... |
| olcnd 876 | A lemma for Conjunctive No... |
| unitreslOLD 877 | Obsolete version of ~ olcn... |
| orcnd 878 | A lemma for Conjunctive No... |
| mtord 879 | A modus tollens deduction ... |
| pm3.2ni 880 | Infer negated disjunction ... |
| pm2.45 881 | Theorem *2.45 of [Whitehea... |
| pm2.46 882 | Theorem *2.46 of [Whitehea... |
| pm2.47 883 | Theorem *2.47 of [Whitehea... |
| pm2.48 884 | Theorem *2.48 of [Whitehea... |
| pm2.49 885 | Theorem *2.49 of [Whitehea... |
| norbi 886 | If neither of two proposit... |
| nbior 887 | If two propositions are no... |
| orel1 888 | Elimination of disjunction... |
| pm2.25 889 | Theorem *2.25 of [Whitehea... |
| orel2 890 | Elimination of disjunction... |
| pm2.67-2 891 | Slight generalization of T... |
| pm2.67 892 | Theorem *2.67 of [Whitehea... |
| curryax 893 | A non-intuitionistic posit... |
| exmid 894 | Law of excluded middle, al... |
| exmidd 895 | Law of excluded middle in ... |
| pm2.1 896 | Theorem *2.1 of [Whitehead... |
| pm2.13 897 | Theorem *2.13 of [Whitehea... |
| pm2.621 898 | Theorem *2.621 of [Whitehe... |
| pm2.62 899 | Theorem *2.62 of [Whitehea... |
| pm2.68 900 | Theorem *2.68 of [Whitehea... |
| dfor2 901 | Logical 'or' expressed in ... |
| pm2.07 902 | Theorem *2.07 of [Whitehea... |
| pm1.2 903 | Axiom *1.2 of [WhiteheadRu... |
| oridm 904 | Idempotent law for disjunc... |
| pm4.25 905 | Theorem *4.25 of [Whitehea... |
| pm2.4 906 | Theorem *2.4 of [Whitehead... |
| pm2.41 907 | Theorem *2.41 of [Whitehea... |
| orim12i 908 | Disjoin antecedents and co... |
| orim1i 909 | Introduce disjunct to both... |
| orim2i 910 | Introduce disjunct to both... |
| orim12dALT 911 | Alternate proof of ~ orim1... |
| orbi2i 912 | Inference adding a left di... |
| orbi1i 913 | Inference adding a right d... |
| orbi12i 914 | Infer the disjunction of t... |
| orbi2d 915 | Deduction adding a left di... |
| orbi1d 916 | Deduction adding a right d... |
| orbi1 917 | Theorem *4.37 of [Whitehea... |
| orbi12d 918 | Deduction joining two equi... |
| pm1.5 919 | Axiom *1.5 (Assoc) of [Whi... |
| or12 920 | Swap two disjuncts. (Cont... |
| orass 921 | Associative law for disjun... |
| pm2.31 922 | Theorem *2.31 of [Whitehea... |
| pm2.32 923 | Theorem *2.32 of [Whitehea... |
| pm2.3 924 | Theorem *2.3 of [Whitehead... |
| or32 925 | A rearrangement of disjunc... |
| or4 926 | Rearrangement of 4 disjunc... |
| or42 927 | Rearrangement of 4 disjunc... |
| orordi 928 | Distribution of disjunctio... |
| orordir 929 | Distribution of disjunctio... |
| orimdi 930 | Disjunction distributes ov... |
| pm2.76 931 | Theorem *2.76 of [Whitehea... |
| pm2.85 932 | Theorem *2.85 of [Whitehea... |
| pm2.75 933 | Theorem *2.75 of [Whitehea... |
| pm4.78 934 | Implication distributes ov... |
| biort 935 | A disjunction with a true ... |
| biorf 936 | A wff is equivalent to its... |
| biortn 937 | A wff is equivalent to its... |
| biorfi 938 | A wff is equivalent to its... |
| pm2.26 939 | Theorem *2.26 of [Whitehea... |
| pm2.63 940 | Theorem *2.63 of [Whitehea... |
| pm2.64 941 | Theorem *2.64 of [Whitehea... |
| pm2.42 942 | Theorem *2.42 of [Whitehea... |
| pm5.11g 943 | A general instance of Theo... |
| pm5.11 944 | Theorem *5.11 of [Whitehea... |
| pm5.12 945 | Theorem *5.12 of [Whitehea... |
| pm5.14 946 | Theorem *5.14 of [Whitehea... |
| pm5.13 947 | Theorem *5.13 of [Whitehea... |
| pm5.55 948 | Theorem *5.55 of [Whitehea... |
| pm4.72 949 | Implication in terms of bi... |
| imimorb 950 | Simplify an implication be... |
| oibabs 951 | Absorption of disjunction ... |
| orbidi 952 | Disjunction distributes ov... |
| pm5.7 953 | Disjunction distributes ov... |
| jaao 954 | Inference conjoining and d... |
| jaoa 955 | Inference disjoining and c... |
| jaoian 956 | Inference disjoining the a... |
| jaodan 957 | Deduction disjoining the a... |
| mpjaodan 958 | Eliminate a disjunction in... |
| pm3.44 959 | Theorem *3.44 of [Whitehea... |
| jao 960 | Disjunction of antecedents... |
| jaob 961 | Disjunction of antecedents... |
| pm4.77 962 | Theorem *4.77 of [Whitehea... |
| pm3.48 963 | Theorem *3.48 of [Whitehea... |
| orim12d 964 | Disjoin antecedents and co... |
| orim1d 965 | Disjoin antecedents and co... |
| orim2d 966 | Disjoin antecedents and co... |
| orim2 967 | Axiom *1.6 (Sum) of [White... |
| pm2.38 968 | Theorem *2.38 of [Whitehea... |
| pm2.36 969 | Theorem *2.36 of [Whitehea... |
| pm2.37 970 | Theorem *2.37 of [Whitehea... |
| pm2.81 971 | Theorem *2.81 of [Whitehea... |
| pm2.8 972 | Theorem *2.8 of [Whitehead... |
| pm2.73 973 | Theorem *2.73 of [Whitehea... |
| pm2.74 974 | Theorem *2.74 of [Whitehea... |
| pm2.82 975 | Theorem *2.82 of [Whitehea... |
| pm4.39 976 | Theorem *4.39 of [Whitehea... |
| animorl 977 | Conjunction implies disjun... |
| animorr 978 | Conjunction implies disjun... |
| animorlr 979 | Conjunction implies disjun... |
| animorrl 980 | Conjunction implies disjun... |
| ianor 981 | Negated conjunction in ter... |
| anor 982 | Conjunction in terms of di... |
| ioran 983 | Negated disjunction in ter... |
| pm4.52 984 | Theorem *4.52 of [Whitehea... |
| pm4.53 985 | Theorem *4.53 of [Whitehea... |
| pm4.54 986 | Theorem *4.54 of [Whitehea... |
| pm4.55 987 | Theorem *4.55 of [Whitehea... |
| pm4.56 988 | Theorem *4.56 of [Whitehea... |
| oran 989 | Disjunction in terms of co... |
| pm4.57 990 | Theorem *4.57 of [Whitehea... |
| pm3.1 991 | Theorem *3.1 of [Whitehead... |
| pm3.11 992 | Theorem *3.11 of [Whitehea... |
| pm3.12 993 | Theorem *3.12 of [Whitehea... |
| pm3.13 994 | Theorem *3.13 of [Whitehea... |
| pm3.14 995 | Theorem *3.14 of [Whitehea... |
| pm4.44 996 | Theorem *4.44 of [Whitehea... |
| pm4.45 997 | Theorem *4.45 of [Whitehea... |
| orabs 998 | Absorption of redundant in... |
| oranabs 999 | Absorb a disjunct into a c... |
| pm5.61 1000 | Theorem *5.61 of [Whitehea... |
| pm5.6 1001 | Conjunction in antecedent ... |
| orcanai 1002 | Change disjunction in cons... |
| pm4.79 1003 | Theorem *4.79 of [Whitehea... |
| pm5.53 1004 | Theorem *5.53 of [Whitehea... |
| ordi 1005 | Distributive law for disju... |
| ordir 1006 | Distributive law for disju... |
| andi 1007 | Distributive law for conju... |
| andir 1008 | Distributive law for conju... |
| orddi 1009 | Double distributive law fo... |
| anddi 1010 | Double distributive law fo... |
| pm5.17 1011 | Theorem *5.17 of [Whitehea... |
| pm5.15 1012 | Theorem *5.15 of [Whitehea... |
| pm5.16 1013 | Theorem *5.16 of [Whitehea... |
| xor 1014 | Two ways to express exclus... |
| nbi2 1015 | Two ways to express "exclu... |
| xordi 1016 | Conjunction distributes ov... |
| pm5.54 1017 | Theorem *5.54 of [Whitehea... |
| pm5.62 1018 | Theorem *5.62 of [Whitehea... |
| pm5.63 1019 | Theorem *5.63 of [Whitehea... |
| niabn 1020 | Miscellaneous inference re... |
| ninba 1021 | Miscellaneous inference re... |
| pm4.43 1022 | Theorem *4.43 of [Whitehea... |
| pm4.82 1023 | Theorem *4.82 of [Whitehea... |
| pm4.83 1024 | Theorem *4.83 of [Whitehea... |
| pclem6 1025 | Negation inferred from emb... |
| bigolden 1026 | Dijkstra-Scholten's Golden... |
| pm5.71 1027 | Theorem *5.71 of [Whitehea... |
| pm5.75 1028 | Theorem *5.75 of [Whitehea... |
| ecase2d 1029 | Deduction for elimination ... |
| ecase2dOLD 1030 | Obsolete version of ~ ecas... |
| ecase3 1031 | Inference for elimination ... |
| ecase 1032 | Inference for elimination ... |
| ecase3d 1033 | Deduction for elimination ... |
| ecased 1034 | Deduction for elimination ... |
| ecase3ad 1035 | Deduction for elimination ... |
| ecase3adOLD 1036 | Obsolete version of ~ ecas... |
| ccase 1037 | Inference for combining ca... |
| ccased 1038 | Deduction for combining ca... |
| ccase2 1039 | Inference for combining ca... |
| 4cases 1040 | Inference eliminating two ... |
| 4casesdan 1041 | Deduction eliminating two ... |
| cases 1042 | Case disjunction according... |
| dedlem0a 1043 | Lemma for an alternate ver... |
| dedlem0b 1044 | Lemma for an alternate ver... |
| dedlema 1045 | Lemma for weak deduction t... |
| dedlemb 1046 | Lemma for weak deduction t... |
| cases2 1047 | Case disjunction according... |
| cases2ALT 1048 | Alternate proof of ~ cases... |
| dfbi3 1049 | An alternate definition of... |
| pm5.24 1050 | Theorem *5.24 of [Whitehea... |
| 4exmid 1051 | The disjunction of the fou... |
| consensus 1052 | The consensus theorem. Th... |
| pm4.42 1053 | Theorem *4.42 of [Whitehea... |
| prlem1 1054 | A specialized lemma for se... |
| prlem2 1055 | A specialized lemma for se... |
| oplem1 1056 | A specialized lemma for se... |
| dn1 1057 | A single axiom for Boolean... |
| bianir 1058 | A closed form of ~ mpbir ,... |
| jaoi2 1059 | Inference removing a negat... |
| jaoi3 1060 | Inference separating a dis... |
| ornld 1061 | Selecting one statement fr... |
| dfifp2 1064 | Alternate definition of th... |
| dfifp3 1065 | Alternate definition of th... |
| dfifp4 1066 | Alternate definition of th... |
| dfifp5 1067 | Alternate definition of th... |
| dfifp6 1068 | Alternate definition of th... |
| dfifp7 1069 | Alternate definition of th... |
| ifpdfbi 1070 | Define the biconditional a... |
| anifp 1071 | The conditional operator i... |
| ifpor 1072 | The conditional operator i... |
| ifpn 1073 | Conditional operator for t... |
| ifpnOLD 1074 | Obsolete version of ~ ifpn... |
| ifptru 1075 | Value of the conditional o... |
| ifpfal 1076 | Value of the conditional o... |
| ifpid 1077 | Value of the conditional o... |
| casesifp 1078 | Version of ~ cases express... |
| ifpbi123d 1079 | Equivalence deduction for ... |
| ifpbi123dOLD 1080 | Obsolete version of ~ ifpb... |
| ifpbi23d 1081 | Equivalence deduction for ... |
| ifpimpda 1082 | Separation of the values o... |
| 1fpid3 1083 | The value of the condition... |
| elimh 1084 | Hypothesis builder for the... |
| dedt 1085 | The weak deduction theorem... |
| con3ALT 1086 | Proof of ~ con3 from its a... |
| 3orass 1091 | Associative law for triple... |
| 3orel1 1092 | Partial elimination of a t... |
| 3orrot 1093 | Rotation law for triple di... |
| 3orcoma 1094 | Commutation law for triple... |
| 3orcomb 1095 | Commutation law for triple... |
| 3anass 1096 | Associative law for triple... |
| 3anan12 1097 | Convert triple conjunction... |
| 3anan32 1098 | Convert triple conjunction... |
| 3ancoma 1099 | Commutation law for triple... |
| 3ancomb 1100 | Commutation law for triple... |
| 3anrot 1101 | Rotation law for triple co... |
| 3anrev 1102 | Reversal law for triple co... |
| anandi3 1103 | Distribution of triple con... |
| anandi3r 1104 | Distribution of triple con... |
| 3anidm 1105 | Idempotent law for conjunc... |
| 3an4anass 1106 | Associative law for four c... |
| 3ioran 1107 | Negated triple disjunction... |
| 3ianor 1108 | Negated triple conjunction... |
| 3anor 1109 | Triple conjunction express... |
| 3oran 1110 | Triple disjunction in term... |
| 3impa 1111 | Importation from double to... |
| 3imp 1112 | Importation inference. (C... |
| 3imp31 1113 | The importation inference ... |
| 3imp231 1114 | Importation inference. (C... |
| 3imp21 1115 | The importation inference ... |
| 3impb 1116 | Importation from double to... |
| 3impib 1117 | Importation to triple conj... |
| 3impia 1118 | Importation to triple conj... |
| 3expa 1119 | Exportation from triple to... |
| 3exp 1120 | Exportation inference. (C... |
| 3expb 1121 | Exportation from triple to... |
| 3expia 1122 | Exportation from triple co... |
| 3expib 1123 | Exportation from triple co... |
| 3com12 1124 | Commutation in antecedent.... |
| 3com13 1125 | Commutation in antecedent.... |
| 3comr 1126 | Commutation in antecedent.... |
| 3com23 1127 | Commutation in antecedent.... |
| 3coml 1128 | Commutation in antecedent.... |
| 3jca 1129 | Join consequents with conj... |
| 3jcad 1130 | Deduction conjoining the c... |
| 3adant1 1131 | Deduction adding a conjunc... |
| 3adant2 1132 | Deduction adding a conjunc... |
| 3adant3 1133 | Deduction adding a conjunc... |
| 3ad2ant1 1134 | Deduction adding conjuncts... |
| 3ad2ant2 1135 | Deduction adding conjuncts... |
| 3ad2ant3 1136 | Deduction adding conjuncts... |
| simp1 1137 | Simplification of triple c... |
| simp2 1138 | Simplification of triple c... |
| simp3 1139 | Simplification of triple c... |
| simp1i 1140 | Infer a conjunct from a tr... |
| simp2i 1141 | Infer a conjunct from a tr... |
| simp3i 1142 | Infer a conjunct from a tr... |
| simp1d 1143 | Deduce a conjunct from a t... |
| simp2d 1144 | Deduce a conjunct from a t... |
| simp3d 1145 | Deduce a conjunct from a t... |
| simp1bi 1146 | Deduce a conjunct from a t... |
| simp2bi 1147 | Deduce a conjunct from a t... |
| simp3bi 1148 | Deduce a conjunct from a t... |
| 3simpa 1149 | Simplification of triple c... |
| 3simpb 1150 | Simplification of triple c... |
| 3simpc 1151 | Simplification of triple c... |
| 3anim123i 1152 | Join antecedents and conse... |
| 3anim1i 1153 | Add two conjuncts to antec... |
| 3anim2i 1154 | Add two conjuncts to antec... |
| 3anim3i 1155 | Add two conjuncts to antec... |
| 3anbi123i 1156 | Join 3 biconditionals with... |
| 3orbi123i 1157 | Join 3 biconditionals with... |
| 3anbi1i 1158 | Inference adding two conju... |
| 3anbi2i 1159 | Inference adding two conju... |
| 3anbi3i 1160 | Inference adding two conju... |
| syl3an 1161 | A triple syllogism inferen... |
| syl3anb 1162 | A triple syllogism inferen... |
| syl3anbr 1163 | A triple syllogism inferen... |
| syl3an1 1164 | A syllogism inference. (C... |
| syl3an2 1165 | A syllogism inference. (C... |
| syl3an3 1166 | A syllogism inference. (C... |
| 3adantl1 1167 | Deduction adding a conjunc... |
| 3adantl2 1168 | Deduction adding a conjunc... |
| 3adantl3 1169 | Deduction adding a conjunc... |
| 3adantr1 1170 | Deduction adding a conjunc... |
| 3adantr2 1171 | Deduction adding a conjunc... |
| 3adantr3 1172 | Deduction adding a conjunc... |
| ad4ant123 1173 | Deduction adding conjuncts... |
| ad4ant124 1174 | Deduction adding conjuncts... |
| ad4ant134 1175 | Deduction adding conjuncts... |
| ad4ant234 1176 | Deduction adding conjuncts... |
| 3adant1l 1177 | Deduction adding a conjunc... |
| 3adant1r 1178 | Deduction adding a conjunc... |
| 3adant2l 1179 | Deduction adding a conjunc... |
| 3adant2r 1180 | Deduction adding a conjunc... |
| 3adant3l 1181 | Deduction adding a conjunc... |
| 3adant3r 1182 | Deduction adding a conjunc... |
| 3adant3r1 1183 | Deduction adding a conjunc... |
| 3adant3r2 1184 | Deduction adding a conjunc... |
| 3adant3r3 1185 | Deduction adding a conjunc... |
| 3ad2antl1 1186 | Deduction adding conjuncts... |
| 3ad2antl2 1187 | Deduction adding conjuncts... |
| 3ad2antl3 1188 | Deduction adding conjuncts... |
| 3ad2antr1 1189 | Deduction adding conjuncts... |
| 3ad2antr2 1190 | Deduction adding conjuncts... |
| 3ad2antr3 1191 | Deduction adding conjuncts... |
| simpl1 1192 | Simplification of conjunct... |
| simpl2 1193 | Simplification of conjunct... |
| simpl3 1194 | Simplification of conjunct... |
| simpr1 1195 | Simplification of conjunct... |
| simpr2 1196 | Simplification of conjunct... |
| simpr3 1197 | Simplification of conjunct... |
| simp1l 1198 | Simplification of triple c... |
| simp1r 1199 | Simplification of triple c... |
| simp2l 1200 | Simplification of triple c... |
| simp2r 1201 | Simplification of triple c... |
| simp3l 1202 | Simplification of triple c... |
| simp3r 1203 | Simplification of triple c... |
| simp11 1204 | Simplification of doubly t... |
| simp12 1205 | Simplification of doubly t... |
| simp13 1206 | Simplification of doubly t... |
| simp21 1207 | Simplification of doubly t... |
| simp22 1208 | Simplification of doubly t... |
| simp23 1209 | Simplification of doubly t... |
| simp31 1210 | Simplification of doubly t... |
| simp32 1211 | Simplification of doubly t... |
| simp33 1212 | Simplification of doubly t... |
| simpll1 1213 | Simplification of conjunct... |
| simpll2 1214 | Simplification of conjunct... |
| simpll3 1215 | Simplification of conjunct... |
| simplr1 1216 | Simplification of conjunct... |
| simplr2 1217 | Simplification of conjunct... |
| simplr3 1218 | Simplification of conjunct... |
| simprl1 1219 | Simplification of conjunct... |
| simprl2 1220 | Simplification of conjunct... |
| simprl3 1221 | Simplification of conjunct... |
| simprr1 1222 | Simplification of conjunct... |
| simprr2 1223 | Simplification of conjunct... |
| simprr3 1224 | Simplification of conjunct... |
| simpl1l 1225 | Simplification of conjunct... |
| simpl1r 1226 | Simplification of conjunct... |
| simpl2l 1227 | Simplification of conjunct... |
| simpl2r 1228 | Simplification of conjunct... |
| simpl3l 1229 | Simplification of conjunct... |
| simpl3r 1230 | Simplification of conjunct... |
| simpr1l 1231 | Simplification of conjunct... |
| simpr1r 1232 | Simplification of conjunct... |
| simpr2l 1233 | Simplification of conjunct... |
| simpr2r 1234 | Simplification of conjunct... |
| simpr3l 1235 | Simplification of conjunct... |
| simpr3r 1236 | Simplification of conjunct... |
| simp1ll 1237 | Simplification of conjunct... |
| simp1lr 1238 | Simplification of conjunct... |
| simp1rl 1239 | Simplification of conjunct... |
| simp1rr 1240 | Simplification of conjunct... |
| simp2ll 1241 | Simplification of conjunct... |
| simp2lr 1242 | Simplification of conjunct... |
| simp2rl 1243 | Simplification of conjunct... |
| simp2rr 1244 | Simplification of conjunct... |
| simp3ll 1245 | Simplification of conjunct... |
| simp3lr 1246 | Simplification of conjunct... |
| simp3rl 1247 | Simplification of conjunct... |
| simp3rr 1248 | Simplification of conjunct... |
| simpl11 1249 | Simplification of conjunct... |
| simpl12 1250 | Simplification of conjunct... |
| simpl13 1251 | Simplification of conjunct... |
| simpl21 1252 | Simplification of conjunct... |
| simpl22 1253 | Simplification of conjunct... |
| simpl23 1254 | Simplification of conjunct... |
| simpl31 1255 | Simplification of conjunct... |
| simpl32 1256 | Simplification of conjunct... |
| simpl33 1257 | Simplification of conjunct... |
| simpr11 1258 | Simplification of conjunct... |
| simpr12 1259 | Simplification of conjunct... |
| simpr13 1260 | Simplification of conjunct... |
| simpr21 1261 | Simplification of conjunct... |
| simpr22 1262 | Simplification of conjunct... |
| simpr23 1263 | Simplification of conjunct... |
| simpr31 1264 | Simplification of conjunct... |
| simpr32 1265 | Simplification of conjunct... |
| simpr33 1266 | Simplification of conjunct... |
| simp1l1 1267 | Simplification of conjunct... |
| simp1l2 1268 | Simplification of conjunct... |
| simp1l3 1269 | Simplification of conjunct... |
| simp1r1 1270 | Simplification of conjunct... |
| simp1r2 1271 | Simplification of conjunct... |
| simp1r3 1272 | Simplification of conjunct... |
| simp2l1 1273 | Simplification of conjunct... |
| simp2l2 1274 | Simplification of conjunct... |
| simp2l3 1275 | Simplification of conjunct... |
| simp2r1 1276 | Simplification of conjunct... |
| simp2r2 1277 | Simplification of conjunct... |
| simp2r3 1278 | Simplification of conjunct... |
| simp3l1 1279 | Simplification of conjunct... |
| simp3l2 1280 | Simplification of conjunct... |
| simp3l3 1281 | Simplification of conjunct... |
| simp3r1 1282 | Simplification of conjunct... |
| simp3r2 1283 | Simplification of conjunct... |
| simp3r3 1284 | Simplification of conjunct... |
| simp11l 1285 | Simplification of conjunct... |
| simp11r 1286 | Simplification of conjunct... |
| simp12l 1287 | Simplification of conjunct... |
| simp12r 1288 | Simplification of conjunct... |
| simp13l 1289 | Simplification of conjunct... |
| simp13r 1290 | Simplification of conjunct... |
| simp21l 1291 | Simplification of conjunct... |
| simp21r 1292 | Simplification of conjunct... |
| simp22l 1293 | Simplification of conjunct... |
| simp22r 1294 | Simplification of conjunct... |
| simp23l 1295 | Simplification of conjunct... |
| simp23r 1296 | Simplification of conjunct... |
| simp31l 1297 | Simplification of conjunct... |
| simp31r 1298 | Simplification of conjunct... |
| simp32l 1299 | Simplification of conjunct... |
| simp32r 1300 | Simplification of conjunct... |
| simp33l 1301 | Simplification of conjunct... |
| simp33r 1302 | Simplification of conjunct... |
| simp111 1303 | Simplification of conjunct... |
| simp112 1304 | Simplification of conjunct... |
| simp113 1305 | Simplification of conjunct... |
| simp121 1306 | Simplification of conjunct... |
| simp122 1307 | Simplification of conjunct... |
| simp123 1308 | Simplification of conjunct... |
| simp131 1309 | Simplification of conjunct... |
| simp132 1310 | Simplification of conjunct... |
| simp133 1311 | Simplification of conjunct... |
| simp211 1312 | Simplification of conjunct... |
| simp212 1313 | Simplification of conjunct... |
| simp213 1314 | Simplification of conjunct... |
| simp221 1315 | Simplification of conjunct... |
| simp222 1316 | Simplification of conjunct... |
| simp223 1317 | Simplification of conjunct... |
| simp231 1318 | Simplification of conjunct... |
| simp232 1319 | Simplification of conjunct... |
| simp233 1320 | Simplification of conjunct... |
| simp311 1321 | Simplification of conjunct... |
| simp312 1322 | Simplification of conjunct... |
| simp313 1323 | Simplification of conjunct... |
| simp321 1324 | Simplification of conjunct... |
| simp322 1325 | Simplification of conjunct... |
| simp323 1326 | Simplification of conjunct... |
| simp331 1327 | Simplification of conjunct... |
| simp332 1328 | Simplification of conjunct... |
| simp333 1329 | Simplification of conjunct... |
| 3anibar 1330 | Remove a hypothesis from t... |
| 3mix1 1331 | Introduction in triple dis... |
| 3mix2 1332 | Introduction in triple dis... |
| 3mix3 1333 | Introduction in triple dis... |
| 3mix1i 1334 | Introduction in triple dis... |
| 3mix2i 1335 | Introduction in triple dis... |
| 3mix3i 1336 | Introduction in triple dis... |
| 3mix1d 1337 | Deduction introducing trip... |
| 3mix2d 1338 | Deduction introducing trip... |
| 3mix3d 1339 | Deduction introducing trip... |
| 3pm3.2i 1340 | Infer conjunction of premi... |
| pm3.2an3 1341 | Version of ~ pm3.2 for a t... |
| mpbir3an 1342 | Detach a conjunction of tr... |
| mpbir3and 1343 | Detach a conjunction of tr... |
| syl3anbrc 1344 | Syllogism inference. (Con... |
| syl21anbrc 1345 | Syllogism inference. (Con... |
| 3imp3i2an 1346 | An elimination deduction. ... |
| ex3 1347 | Apply ~ ex to a hypothesis... |
| 3imp1 1348 | Importation to left triple... |
| 3impd 1349 | Importation deduction for ... |
| 3imp2 1350 | Importation to right tripl... |
| 3impdi 1351 | Importation inference (und... |
| 3impdir 1352 | Importation inference (und... |
| 3exp1 1353 | Exportation from left trip... |
| 3expd 1354 | Exportation deduction for ... |
| 3exp2 1355 | Exportation from right tri... |
| exp5o 1356 | A triple exportation infer... |
| exp516 1357 | A triple exportation infer... |
| exp520 1358 | A triple exportation infer... |
| 3impexp 1359 | Version of ~ impexp for a ... |
| 3an1rs 1360 | Swap conjuncts. (Contribu... |
| 3anassrs 1361 | Associative law for conjun... |
| ad5ant245 1362 | Deduction adding conjuncts... |
| ad5ant234 1363 | Deduction adding conjuncts... |
| ad5ant235 1364 | Deduction adding conjuncts... |
| ad5ant123 1365 | Deduction adding conjuncts... |
| ad5ant124 1366 | Deduction adding conjuncts... |
| ad5ant125 1367 | Deduction adding conjuncts... |
| ad5ant134 1368 | Deduction adding conjuncts... |
| ad5ant135 1369 | Deduction adding conjuncts... |
| ad5ant145 1370 | Deduction adding conjuncts... |
| ad5ant2345 1371 | Deduction adding conjuncts... |
| syl3anc 1372 | Syllogism combined with co... |
| syl13anc 1373 | Syllogism combined with co... |
| syl31anc 1374 | Syllogism combined with co... |
| syl112anc 1375 | Syllogism combined with co... |
| syl121anc 1376 | Syllogism combined with co... |
| syl211anc 1377 | Syllogism combined with co... |
| syl23anc 1378 | Syllogism combined with co... |
| syl32anc 1379 | Syllogism combined with co... |
| syl122anc 1380 | Syllogism combined with co... |
| syl212anc 1381 | Syllogism combined with co... |
| syl221anc 1382 | Syllogism combined with co... |
| syl113anc 1383 | Syllogism combined with co... |
| syl131anc 1384 | Syllogism combined with co... |
| syl311anc 1385 | Syllogism combined with co... |
| syl33anc 1386 | Syllogism combined with co... |
| syl222anc 1387 | Syllogism combined with co... |
| syl123anc 1388 | Syllogism combined with co... |
| syl132anc 1389 | Syllogism combined with co... |
| syl213anc 1390 | Syllogism combined with co... |
| syl231anc 1391 | Syllogism combined with co... |
| syl312anc 1392 | Syllogism combined with co... |
| syl321anc 1393 | Syllogism combined with co... |
| syl133anc 1394 | Syllogism combined with co... |
| syl313anc 1395 | Syllogism combined with co... |
| syl331anc 1396 | Syllogism combined with co... |
| syl223anc 1397 | Syllogism combined with co... |
| syl232anc 1398 | Syllogism combined with co... |
| syl322anc 1399 | Syllogism combined with co... |
| syl233anc 1400 | Syllogism combined with co... |
| syl323anc 1401 | Syllogism combined with co... |
| syl332anc 1402 | Syllogism combined with co... |
| syl333anc 1403 | A syllogism inference comb... |
| syl3an1b 1404 | A syllogism inference. (C... |
| syl3an2b 1405 | A syllogism inference. (C... |
| syl3an3b 1406 | A syllogism inference. (C... |
| syl3an1br 1407 | A syllogism inference. (C... |
| syl3an2br 1408 | A syllogism inference. (C... |
| syl3an3br 1409 | A syllogism inference. (C... |
| syld3an3 1410 | A syllogism inference. (C... |
| syld3an1 1411 | A syllogism inference. (C... |
| syld3an2 1412 | A syllogism inference. (C... |
| syl3anl1 1413 | A syllogism inference. (C... |
| syl3anl2 1414 | A syllogism inference. (C... |
| syl3anl3 1415 | A syllogism inference. (C... |
| syl3anl 1416 | A triple syllogism inferen... |
| syl3anr1 1417 | A syllogism inference. (C... |
| syl3anr2 1418 | A syllogism inference. (C... |
| syl3anr3 1419 | A syllogism inference. (C... |
| 3anidm12 1420 | Inference from idempotent ... |
| 3anidm13 1421 | Inference from idempotent ... |
| 3anidm23 1422 | Inference from idempotent ... |
| syl2an3an 1423 | ~ syl3an with antecedents ... |
| syl2an23an 1424 | Deduction related to ~ syl... |
| 3ori 1425 | Infer implication from tri... |
| 3jao 1426 | Disjunction of three antec... |
| 3jaob 1427 | Disjunction of three antec... |
| 3jaoi 1428 | Disjunction of three antec... |
| 3jaod 1429 | Disjunction of three antec... |
| 3jaoian 1430 | Disjunction of three antec... |
| 3jaodan 1431 | Disjunction of three antec... |
| mpjao3dan 1432 | Eliminate a three-way disj... |
| mpjao3danOLD 1433 | Obsolete version of ~ mpja... |
| 3jaao 1434 | Inference conjoining and d... |
| syl3an9b 1435 | Nested syllogism inference... |
| 3orbi123d 1436 | Deduction joining 3 equiva... |
| 3anbi123d 1437 | Deduction joining 3 equiva... |
| 3anbi12d 1438 | Deduction conjoining and a... |
| 3anbi13d 1439 | Deduction conjoining and a... |
| 3anbi23d 1440 | Deduction conjoining and a... |
| 3anbi1d 1441 | Deduction adding conjuncts... |
| 3anbi2d 1442 | Deduction adding conjuncts... |
| 3anbi3d 1443 | Deduction adding conjuncts... |
| 3anim123d 1444 | Deduction joining 3 implic... |
| 3orim123d 1445 | Deduction joining 3 implic... |
| an6 1446 | Rearrangement of 6 conjunc... |
| 3an6 1447 | Analogue of ~ an4 for trip... |
| 3or6 1448 | Analogue of ~ or4 for trip... |
| mp3an1 1449 | An inference based on modu... |
| mp3an2 1450 | An inference based on modu... |
| mp3an3 1451 | An inference based on modu... |
| mp3an12 1452 | An inference based on modu... |
| mp3an13 1453 | An inference based on modu... |
| mp3an23 1454 | An inference based on modu... |
| mp3an1i 1455 | An inference based on modu... |
| mp3anl1 1456 | An inference based on modu... |
| mp3anl2 1457 | An inference based on modu... |
| mp3anl3 1458 | An inference based on modu... |
| mp3anr1 1459 | An inference based on modu... |
| mp3anr2 1460 | An inference based on modu... |
| mp3anr3 1461 | An inference based on modu... |
| mp3an 1462 | An inference based on modu... |
| mpd3an3 1463 | An inference based on modu... |
| mpd3an23 1464 | An inference based on modu... |
| mp3and 1465 | A deduction based on modus... |
| mp3an12i 1466 | ~ mp3an with antecedents i... |
| mp3an2i 1467 | ~ mp3an with antecedents i... |
| mp3an3an 1468 | ~ mp3an with antecedents i... |
| mp3an2ani 1469 | An elimination deduction. ... |
| biimp3a 1470 | Infer implication from a l... |
| biimp3ar 1471 | Infer implication from a l... |
| 3anandis 1472 | Inference that undistribut... |
| 3anandirs 1473 | Inference that undistribut... |
| ecase23d 1474 | Deduction for elimination ... |
| 3ecase 1475 | Inference for elimination ... |
| 3bior1fd 1476 | A disjunction is equivalen... |
| 3bior1fand 1477 | A disjunction is equivalen... |
| 3bior2fd 1478 | A wff is equivalent to its... |
| 3biant1d 1479 | A conjunction is equivalen... |
| intn3an1d 1480 | Introduction of a triple c... |
| intn3an2d 1481 | Introduction of a triple c... |
| intn3an3d 1482 | Introduction of a triple c... |
| an3andi 1483 | Distribution of conjunctio... |
| an33rean 1484 | Rearrange a 9-fold conjunc... |
| an33reanOLD 1485 | Obsolete version of ~ an33... |
| nanan 1488 | Conjunction in terms of al... |
| dfnan2 1489 | Alternative denial in term... |
| nanor 1490 | Alternative denial in term... |
| nancom 1491 | Alternative denial is comm... |
| nannan 1492 | Nested alternative denials... |
| nanim 1493 | Implication in terms of al... |
| nannot 1494 | Negation in terms of alter... |
| nanbi 1495 | Biconditional in terms of ... |
| nanbi1 1496 | Introduce a right anti-con... |
| nanbi2 1497 | Introduce a left anti-conj... |
| nanbi12 1498 | Join two logical equivalen... |
| nanbi1i 1499 | Introduce a right anti-con... |
| nanbi2i 1500 | Introduce a left anti-conj... |
| nanbi12i 1501 | Join two logical equivalen... |
| nanbi1d 1502 | Introduce a right anti-con... |
| nanbi2d 1503 | Introduce a left anti-conj... |
| nanbi12d 1504 | Join two logical equivalen... |
| nanass 1505 | A characterization of when... |
| xnor 1508 | Two ways to write XNOR (ex... |
| xorcom 1509 | The connector ` \/_ ` is c... |
| xorcomOLD 1510 | Obsolete version of ~ xorc... |
| xorass 1511 | The connector ` \/_ ` is a... |
| excxor 1512 | This tautology shows that ... |
| xor2 1513 | Two ways to express "exclu... |
| xoror 1514 | Exclusive disjunction impl... |
| xornan 1515 | Exclusive disjunction impl... |
| xornan2 1516 | XOR implies NAND (written ... |
| xorneg2 1517 | The connector ` \/_ ` is n... |
| xorneg1 1518 | The connector ` \/_ ` is n... |
| xorneg 1519 | The connector ` \/_ ` is u... |
| xorbi12i 1520 | Equality property for excl... |
| xorbi12iOLD 1521 | Obsolete version of ~ xorb... |
| xorbi12d 1522 | Equality property for excl... |
| anxordi 1523 | Conjunction distributes ov... |
| xorexmid 1524 | Exclusive-or variant of th... |
| norcom 1527 | The connector ` -\/ ` is c... |
| norcomOLD 1528 | Obsolete version of ~ norc... |
| nornot 1529 | ` -. ` is expressible via ... |
| nornotOLD 1530 | Obsolete version of ~ norn... |
| noran 1531 | ` /\ ` is expressible via ... |
| noranOLD 1532 | Obsolete version of ~ nora... |
| noror 1533 | ` \/ ` is expressible via ... |
| nororOLD 1534 | Obsolete version of ~ noro... |
| norasslem1 1535 | This lemma shows the equiv... |
| norasslem2 1536 | This lemma specializes ~ b... |
| norasslem3 1537 | This lemma specializes ~ b... |
| norass 1538 | A characterization of when... |
| norassOLD 1539 | Obsolete version of ~ nora... |
| trujust 1544 | Soundness justification th... |
| tru 1546 | The truth value ` T. ` is ... |
| dftru2 1547 | An alternate definition of... |
| trut 1548 | A proposition is equivalen... |
| mptru 1549 | Eliminate ` T. ` as an ant... |
| tbtru 1550 | A proposition is equivalen... |
| bitru 1551 | A theorem is equivalent to... |
| trud 1552 | Anything implies ` T. ` . ... |
| truan 1553 | True can be removed from a... |
| fal 1556 | The truth value ` F. ` is ... |
| nbfal 1557 | The negation of a proposit... |
| bifal 1558 | A contradiction is equival... |
| falim 1559 | The truth value ` F. ` imp... |
| falimd 1560 | The truth value ` F. ` imp... |
| dfnot 1561 | Given falsum ` F. ` , we c... |
| inegd 1562 | Negation introduction rule... |
| efald 1563 | Deduction based on reducti... |
| pm2.21fal 1564 | If a wff and its negation ... |
| truimtru 1565 | A ` -> ` identity. (Contr... |
| truimfal 1566 | A ` -> ` identity. (Contr... |
| falimtru 1567 | A ` -> ` identity. (Contr... |
| falimfal 1568 | A ` -> ` identity. (Contr... |
| nottru 1569 | A ` -. ` identity. (Contr... |
| notfal 1570 | A ` -. ` identity. (Contr... |
| trubitru 1571 | A ` <-> ` identity. (Cont... |
| falbitru 1572 | A ` <-> ` identity. (Cont... |
| trubifal 1573 | A ` <-> ` identity. (Cont... |
| falbifal 1574 | A ` <-> ` identity. (Cont... |
| truantru 1575 | A ` /\ ` identity. (Contr... |
| truanfal 1576 | A ` /\ ` identity. (Contr... |
| falantru 1577 | A ` /\ ` identity. (Contr... |
| falanfal 1578 | A ` /\ ` identity. (Contr... |
| truortru 1579 | A ` \/ ` identity. (Contr... |
| truorfal 1580 | A ` \/ ` identity. (Contr... |
| falortru 1581 | A ` \/ ` identity. (Contr... |
| falorfal 1582 | A ` \/ ` identity. (Contr... |
| trunantru 1583 | A ` -/\ ` identity. (Cont... |
| trunanfal 1584 | A ` -/\ ` identity. (Cont... |
| falnantru 1585 | A ` -/\ ` identity. (Cont... |
| falnanfal 1586 | A ` -/\ ` identity. (Cont... |
| truxortru 1587 | A ` \/_ ` identity. (Cont... |
| truxorfal 1588 | A ` \/_ ` identity. (Cont... |
| falxortru 1589 | A ` \/_ ` identity. (Cont... |
| falxorfal 1590 | A ` \/_ ` identity. (Cont... |
| trunortru 1591 | A ` -\/ ` identity. (Cont... |
| trunortruOLD 1592 | Obsolete version of ~ trun... |
| trunorfal 1593 | A ` -\/ ` identity. (Cont... |
| trunorfalOLD 1594 | Obsolete version of ~ trun... |
| falnortru 1595 | A ` -\/ ` identity. (Cont... |
| falnorfal 1596 | A ` -\/ ` identity. (Cont... |
| falnorfalOLD 1597 | Obsolete version of ~ faln... |
| hadbi123d 1600 | Equality theorem for the a... |
| hadbi123i 1601 | Equality theorem for the a... |
| hadass 1602 | Associative law for the ad... |
| hadbi 1603 | The adder sum is the same ... |
| hadcoma 1604 | Commutative law for the ad... |
| hadcomaOLD 1605 | Obsolete version of ~ hadc... |
| hadcomb 1606 | Commutative law for the ad... |
| hadrot 1607 | Rotation law for the adder... |
| hadnot 1608 | The adder sum distributes ... |
| had1 1609 | If the first input is true... |
| had0 1610 | If the first input is fals... |
| hadifp 1611 | The value of the adder sum... |
| cador 1614 | The adder carry in disjunc... |
| cadan 1615 | The adder carry in conjunc... |
| cadbi123d 1616 | Equality theorem for the a... |
| cadbi123i 1617 | Equality theorem for the a... |
| cadcoma 1618 | Commutative law for the ad... |
| cadcomb 1619 | Commutative law for the ad... |
| cadrot 1620 | Rotation law for the adder... |
| cadnot 1621 | The adder carry distribute... |
| cad11 1622 | If (at least) two inputs a... |
| cad1 1623 | If one input is true, then... |
| cad0 1624 | If one input is false, the... |
| cad0OLD 1625 | Obsolete version of ~ cad0... |
| cadifp 1626 | The value of the carry is,... |
| cadtru 1627 | The adder carry is true as... |
| minimp 1628 | A single axiom for minimal... |
| minimp-syllsimp 1629 | Derivation of Syll-Simp ( ... |
| minimp-ax1 1630 | Derivation of ~ ax-1 from ... |
| minimp-ax2c 1631 | Derivation of a commuted f... |
| minimp-ax2 1632 | Derivation of ~ ax-2 from ... |
| minimp-pm2.43 1633 | Derivation of ~ pm2.43 (al... |
| impsingle 1634 | The shortest single axiom ... |
| impsingle-step4 1635 | Derivation of impsingle-st... |
| impsingle-step8 1636 | Derivation of impsingle-st... |
| impsingle-ax1 1637 | Derivation of impsingle-ax... |
| impsingle-step15 1638 | Derivation of impsingle-st... |
| impsingle-step18 1639 | Derivation of impsingle-st... |
| impsingle-step19 1640 | Derivation of impsingle-st... |
| impsingle-step20 1641 | Derivation of impsingle-st... |
| impsingle-step21 1642 | Derivation of impsingle-st... |
| impsingle-step22 1643 | Derivation of impsingle-st... |
| impsingle-step25 1644 | Derivation of impsingle-st... |
| impsingle-imim1 1645 | Derivation of impsingle-im... |
| impsingle-peirce 1646 | Derivation of impsingle-pe... |
| tarski-bernays-ax2 1647 | Derivation of ~ ax-2 from ... |
| meredith 1648 | Carew Meredith's sole axio... |
| merlem1 1649 | Step 3 of Meredith's proof... |
| merlem2 1650 | Step 4 of Meredith's proof... |
| merlem3 1651 | Step 7 of Meredith's proof... |
| merlem4 1652 | Step 8 of Meredith's proof... |
| merlem5 1653 | Step 11 of Meredith's proo... |
| merlem6 1654 | Step 12 of Meredith's proo... |
| merlem7 1655 | Between steps 14 and 15 of... |
| merlem8 1656 | Step 15 of Meredith's proo... |
| merlem9 1657 | Step 18 of Meredith's proo... |
| merlem10 1658 | Step 19 of Meredith's proo... |
| merlem11 1659 | Step 20 of Meredith's proo... |
| merlem12 1660 | Step 28 of Meredith's proo... |
| merlem13 1661 | Step 35 of Meredith's proo... |
| luk-1 1662 | 1 of 3 axioms for proposit... |
| luk-2 1663 | 2 of 3 axioms for proposit... |
| luk-3 1664 | 3 of 3 axioms for proposit... |
| luklem1 1665 | Used to rederive standard ... |
| luklem2 1666 | Used to rederive standard ... |
| luklem3 1667 | Used to rederive standard ... |
| luklem4 1668 | Used to rederive standard ... |
| luklem5 1669 | Used to rederive standard ... |
| luklem6 1670 | Used to rederive standard ... |
| luklem7 1671 | Used to rederive standard ... |
| luklem8 1672 | Used to rederive standard ... |
| ax1 1673 | Standard propositional axi... |
| ax2 1674 | Standard propositional axi... |
| ax3 1675 | Standard propositional axi... |
| nic-dfim 1676 | This theorem "defines" imp... |
| nic-dfneg 1677 | This theorem "defines" neg... |
| nic-mp 1678 | Derive Nicod's rule of mod... |
| nic-mpALT 1679 | A direct proof of ~ nic-mp... |
| nic-ax 1680 | Nicod's axiom derived from... |
| nic-axALT 1681 | A direct proof of ~ nic-ax... |
| nic-imp 1682 | Inference for ~ nic-mp usi... |
| nic-idlem1 1683 | Lemma for ~ nic-id . (Con... |
| nic-idlem2 1684 | Lemma for ~ nic-id . Infe... |
| nic-id 1685 | Theorem ~ id expressed wit... |
| nic-swap 1686 | The connector ` -/\ ` is s... |
| nic-isw1 1687 | Inference version of ~ nic... |
| nic-isw2 1688 | Inference for swapping nes... |
| nic-iimp1 1689 | Inference version of ~ nic... |
| nic-iimp2 1690 | Inference version of ~ nic... |
| nic-idel 1691 | Inference to remove the tr... |
| nic-ich 1692 | Chained inference. (Contr... |
| nic-idbl 1693 | Double the terms. Since d... |
| nic-bijust 1694 | Biconditional justificatio... |
| nic-bi1 1695 | Inference to extract one s... |
| nic-bi2 1696 | Inference to extract the o... |
| nic-stdmp 1697 | Derive the standard modus ... |
| nic-luk1 1698 | Proof of ~ luk-1 from ~ ni... |
| nic-luk2 1699 | Proof of ~ luk-2 from ~ ni... |
| nic-luk3 1700 | Proof of ~ luk-3 from ~ ni... |
| lukshef-ax1 1701 | This alternative axiom for... |
| lukshefth1 1702 | Lemma for ~ renicax . (Co... |
| lukshefth2 1703 | Lemma for ~ renicax . (Co... |
| renicax 1704 | A rederivation of ~ nic-ax... |
| tbw-bijust 1705 | Justification for ~ tbw-ne... |
| tbw-negdf 1706 | The definition of negation... |
| tbw-ax1 1707 | The first of four axioms i... |
| tbw-ax2 1708 | The second of four axioms ... |
| tbw-ax3 1709 | The third of four axioms i... |
| tbw-ax4 1710 | The fourth of four axioms ... |
| tbwsyl 1711 | Used to rederive the Lukas... |
| tbwlem1 1712 | Used to rederive the Lukas... |
| tbwlem2 1713 | Used to rederive the Lukas... |
| tbwlem3 1714 | Used to rederive the Lukas... |
| tbwlem4 1715 | Used to rederive the Lukas... |
| tbwlem5 1716 | Used to rederive the Lukas... |
| re1luk1 1717 | ~ luk-1 derived from the T... |
| re1luk2 1718 | ~ luk-2 derived from the T... |
| re1luk3 1719 | ~ luk-3 derived from the T... |
| merco1 1720 | A single axiom for proposi... |
| merco1lem1 1721 | Used to rederive the Tarsk... |
| retbwax4 1722 | ~ tbw-ax4 rederived from ~... |
| retbwax2 1723 | ~ tbw-ax2 rederived from ~... |
| merco1lem2 1724 | Used to rederive the Tarsk... |
| merco1lem3 1725 | Used to rederive the Tarsk... |
| merco1lem4 1726 | Used to rederive the Tarsk... |
| merco1lem5 1727 | Used to rederive the Tarsk... |
| merco1lem6 1728 | Used to rederive the Tarsk... |
| merco1lem7 1729 | Used to rederive the Tarsk... |
| retbwax3 1730 | ~ tbw-ax3 rederived from ~... |
| merco1lem8 1731 | Used to rederive the Tarsk... |
| merco1lem9 1732 | Used to rederive the Tarsk... |
| merco1lem10 1733 | Used to rederive the Tarsk... |
| merco1lem11 1734 | Used to rederive the Tarsk... |
| merco1lem12 1735 | Used to rederive the Tarsk... |
| merco1lem13 1736 | Used to rederive the Tarsk... |
| merco1lem14 1737 | Used to rederive the Tarsk... |
| merco1lem15 1738 | Used to rederive the Tarsk... |
| merco1lem16 1739 | Used to rederive the Tarsk... |
| merco1lem17 1740 | Used to rederive the Tarsk... |
| merco1lem18 1741 | Used to rederive the Tarsk... |
| retbwax1 1742 | ~ tbw-ax1 rederived from ~... |
| merco2 1743 | A single axiom for proposi... |
| mercolem1 1744 | Used to rederive the Tarsk... |
| mercolem2 1745 | Used to rederive the Tarsk... |
| mercolem3 1746 | Used to rederive the Tarsk... |
| mercolem4 1747 | Used to rederive the Tarsk... |
| mercolem5 1748 | Used to rederive the Tarsk... |
| mercolem6 1749 | Used to rederive the Tarsk... |
| mercolem7 1750 | Used to rederive the Tarsk... |
| mercolem8 1751 | Used to rederive the Tarsk... |
| re1tbw1 1752 | ~ tbw-ax1 rederived from ~... |
| re1tbw2 1753 | ~ tbw-ax2 rederived from ~... |
| re1tbw3 1754 | ~ tbw-ax3 rederived from ~... |
| re1tbw4 1755 | ~ tbw-ax4 rederived from ~... |
| rb-bijust 1756 | Justification for ~ rb-imd... |
| rb-imdf 1757 | The definition of implicat... |
| anmp 1758 | Modus ponens for ` { \/ , ... |
| rb-ax1 1759 | The first of four axioms i... |
| rb-ax2 1760 | The second of four axioms ... |
| rb-ax3 1761 | The third of four axioms i... |
| rb-ax4 1762 | The fourth of four axioms ... |
| rbsyl 1763 | Used to rederive the Lukas... |
| rblem1 1764 | Used to rederive the Lukas... |
| rblem2 1765 | Used to rederive the Lukas... |
| rblem3 1766 | Used to rederive the Lukas... |
| rblem4 1767 | Used to rederive the Lukas... |
| rblem5 1768 | Used to rederive the Lukas... |
| rblem6 1769 | Used to rederive the Lukas... |
| rblem7 1770 | Used to rederive the Lukas... |
| re1axmp 1771 | ~ ax-mp derived from Russe... |
| re2luk1 1772 | ~ luk-1 derived from Russe... |
| re2luk2 1773 | ~ luk-2 derived from Russe... |
| re2luk3 1774 | ~ luk-3 derived from Russe... |
| mptnan 1775 | Modus ponendo tollens 1, o... |
| mptxor 1776 | Modus ponendo tollens 2, o... |
| mtpor 1777 | Modus tollendo ponens (inc... |
| mtpxor 1778 | Modus tollendo ponens (ori... |
| stoic1a 1779 | Stoic logic Thema 1 (part ... |
| stoic1b 1780 | Stoic logic Thema 1 (part ... |
| stoic2a 1781 | Stoic logic Thema 2 versio... |
| stoic2b 1782 | Stoic logic Thema 2 versio... |
| stoic3 1783 | Stoic logic Thema 3. Stat... |
| stoic4a 1784 | Stoic logic Thema 4 versio... |
| stoic4b 1785 | Stoic logic Thema 4 versio... |
| alnex 1788 | Universal quantification o... |
| eximal 1789 | An equivalence between an ... |
| nf2 1792 | Alternate definition of no... |
| nf3 1793 | Alternate definition of no... |
| nf4 1794 | Alternate definition of no... |
| nfi 1795 | Deduce that ` x ` is not f... |
| nfri 1796 | Consequence of the definit... |
| nfd 1797 | Deduce that ` x ` is not f... |
| nfrd 1798 | Consequence of the definit... |
| nftht 1799 | Closed form of ~ nfth . (... |
| nfntht 1800 | Closed form of ~ nfnth . ... |
| nfntht2 1801 | Closed form of ~ nfnth . ... |
| gen2 1803 | Generalization applied twi... |
| mpg 1804 | Modus ponens combined with... |
| mpgbi 1805 | Modus ponens on biconditio... |
| mpgbir 1806 | Modus ponens on biconditio... |
| nex 1807 | Generalization rule for ne... |
| nfth 1808 | No variable is (effectivel... |
| nfnth 1809 | No variable is (effectivel... |
| hbth 1810 | No variable is (effectivel... |
| nftru 1811 | The true constant has no f... |
| nffal 1812 | The false constant has no ... |
| sptruw 1813 | Version of ~ sp when ` ph ... |
| altru 1814 | For all sets, ` T. ` is tr... |
| alfal 1815 | For all sets, ` -. F. ` is... |
| alim 1817 | Restatement of Axiom ~ ax-... |
| alimi 1818 | Inference quantifying both... |
| 2alimi 1819 | Inference doubly quantifyi... |
| ala1 1820 | Add an antecedent in a uni... |
| al2im 1821 | Closed form of ~ al2imi . ... |
| al2imi 1822 | Inference quantifying ante... |
| alanimi 1823 | Variant of ~ al2imi with c... |
| alimdh 1824 | Deduction form of Theorem ... |
| albi 1825 | Theorem 19.15 of [Margaris... |
| albii 1826 | Inference adding universal... |
| 2albii 1827 | Inference adding two unive... |
| sylgt 1828 | Closed form of ~ sylg . (... |
| sylg 1829 | A syllogism combined with ... |
| alrimih 1830 | Inference form of Theorem ... |
| hbxfrbi 1831 | A utility lemma to transfe... |
| alex 1832 | Universal quantifier in te... |
| exnal 1833 | Existential quantification... |
| 2nalexn 1834 | Part of theorem *11.5 in [... |
| 2exnaln 1835 | Theorem *11.22 in [Whitehe... |
| 2nexaln 1836 | Theorem *11.25 in [Whitehe... |
| alimex 1837 | An equivalence between an ... |
| aleximi 1838 | A variant of ~ al2imi : in... |
| alexbii 1839 | Biconditional form of ~ al... |
| exim 1840 | Theorem 19.22 of [Margaris... |
| eximi 1841 | Inference adding existenti... |
| 2eximi 1842 | Inference adding two exist... |
| eximii 1843 | Inference associated with ... |
| exa1 1844 | Add an antecedent in an ex... |
| 19.38 1845 | Theorem 19.38 of [Margaris... |
| 19.38a 1846 | Under a nonfreeness hypoth... |
| 19.38b 1847 | Under a nonfreeness hypoth... |
| imnang 1848 | Quantified implication in ... |
| alinexa 1849 | A transformation of quanti... |
| exnalimn 1850 | Existential quantification... |
| alexn 1851 | A relationship between two... |
| 2exnexn 1852 | Theorem *11.51 in [Whitehe... |
| exbi 1853 | Theorem 19.18 of [Margaris... |
| exbii 1854 | Inference adding existenti... |
| 2exbii 1855 | Inference adding two exist... |
| 3exbii 1856 | Inference adding three exi... |
| nfbiit 1857 | Equivalence theorem for th... |
| nfbii 1858 | Equality theorem for the n... |
| nfxfr 1859 | A utility lemma to transfe... |
| nfxfrd 1860 | A utility lemma to transfe... |
| nfnbi 1861 | A variable is nonfree in a... |
| nfnt 1862 | If a variable is nonfree i... |
| nfn 1863 | Inference associated with ... |
| nfnd 1864 | Deduction associated with ... |
| exanali 1865 | A transformation of quanti... |
| 2exanali 1866 | Theorem *11.521 in [Whiteh... |
| exancom 1867 | Commutation of conjunction... |
| exan 1868 | Place a conjunct in the sc... |
| alrimdh 1869 | Deduction form of Theorem ... |
| eximdh 1870 | Deduction from Theorem 19.... |
| nexdh 1871 | Deduction for generalizati... |
| albidh 1872 | Formula-building rule for ... |
| exbidh 1873 | Formula-building rule for ... |
| exsimpl 1874 | Simplification of an exist... |
| exsimpr 1875 | Simplification of an exist... |
| 19.26 1876 | Theorem 19.26 of [Margaris... |
| 19.26-2 1877 | Theorem ~ 19.26 with two q... |
| 19.26-3an 1878 | Theorem ~ 19.26 with tripl... |
| 19.29 1879 | Theorem 19.29 of [Margaris... |
| 19.29r 1880 | Variation of ~ 19.29 . (C... |
| 19.29r2 1881 | Variation of ~ 19.29r with... |
| 19.29x 1882 | Variation of ~ 19.29 with ... |
| 19.35 1883 | Theorem 19.35 of [Margaris... |
| 19.35i 1884 | Inference associated with ... |
| 19.35ri 1885 | Inference associated with ... |
| 19.25 1886 | Theorem 19.25 of [Margaris... |
| 19.30 1887 | Theorem 19.30 of [Margaris... |
| 19.43 1888 | Theorem 19.43 of [Margaris... |
| 19.43OLD 1889 | Obsolete proof of ~ 19.43 ... |
| 19.33 1890 | Theorem 19.33 of [Margaris... |
| 19.33b 1891 | The antecedent provides a ... |
| 19.40 1892 | Theorem 19.40 of [Margaris... |
| 19.40-2 1893 | Theorem *11.42 in [Whitehe... |
| 19.40b 1894 | The antecedent provides a ... |
| albiim 1895 | Split a biconditional and ... |
| 2albiim 1896 | Split a biconditional and ... |
| exintrbi 1897 | Add/remove a conjunct in t... |
| exintr 1898 | Introduce a conjunct in th... |
| alsyl 1899 | Universally quantified and... |
| nfimd 1900 | If in a context ` x ` is n... |
| nfimt 1901 | Closed form of ~ nfim and ... |
| nfim 1902 | If ` x ` is not free in ` ... |
| nfand 1903 | If in a context ` x ` is n... |
| nf3and 1904 | Deduction form of bound-va... |
| nfan 1905 | If ` x ` is not free in ` ... |
| nfnan 1906 | If ` x ` is not free in ` ... |
| nf3an 1907 | If ` x ` is not free in ` ... |
| nfbid 1908 | If in a context ` x ` is n... |
| nfbi 1909 | If ` x ` is not free in ` ... |
| nfor 1910 | If ` x ` is not free in ` ... |
| nf3or 1911 | If ` x ` is not free in ` ... |
| empty 1912 | Two characterizations of t... |
| emptyex 1913 | On the empty domain, any e... |
| emptyal 1914 | On the empty domain, any u... |
| emptynf 1915 | On the empty domain, any v... |
| ax5d 1917 | Version of ~ ax-5 with ant... |
| ax5e 1918 | A rephrasing of ~ ax-5 usi... |
| ax5ea 1919 | If a formula holds for som... |
| nfv 1920 | If ` x ` is not present in... |
| nfvd 1921 | ~ nfv with antecedent. Us... |
| alimdv 1922 | Deduction form of Theorem ... |
| eximdv 1923 | Deduction form of Theorem ... |
| 2alimdv 1924 | Deduction form of Theorem ... |
| 2eximdv 1925 | Deduction form of Theorem ... |
| albidv 1926 | Formula-building rule for ... |
| exbidv 1927 | Formula-building rule for ... |
| nfbidv 1928 | An equality theorem for no... |
| 2albidv 1929 | Formula-building rule for ... |
| 2exbidv 1930 | Formula-building rule for ... |
| 3exbidv 1931 | Formula-building rule for ... |
| 4exbidv 1932 | Formula-building rule for ... |
| alrimiv 1933 | Inference form of Theorem ... |
| alrimivv 1934 | Inference form of Theorem ... |
| alrimdv 1935 | Deduction form of Theorem ... |
| exlimiv 1936 | Inference form of Theorem ... |
| exlimiiv 1937 | Inference (Rule C) associa... |
| exlimivv 1938 | Inference form of Theorem ... |
| exlimdv 1939 | Deduction form of Theorem ... |
| exlimdvv 1940 | Deduction form of Theorem ... |
| exlimddv 1941 | Existential elimination ru... |
| nexdv 1942 | Deduction for generalizati... |
| 2ax5 1943 | Quantification of two vari... |
| stdpc5v 1944 | Version of ~ stdpc5 with a... |
| 19.21v 1945 | Version of ~ 19.21 with a ... |
| 19.32v 1946 | Version of ~ 19.32 with a ... |
| 19.31v 1947 | Version of ~ 19.31 with a ... |
| 19.23v 1948 | Version of ~ 19.23 with a ... |
| 19.23vv 1949 | Theorem ~ 19.23v extended ... |
| pm11.53v 1950 | Version of ~ pm11.53 with ... |
| 19.36imv 1951 | One direction of ~ 19.36v ... |
| 19.36imvOLD 1952 | Obsolete version of ~ 19.3... |
| 19.36iv 1953 | Inference associated with ... |
| 19.37imv 1954 | One direction of ~ 19.37v ... |
| 19.37iv 1955 | Inference associated with ... |
| 19.41v 1956 | Version of ~ 19.41 with a ... |
| 19.41vv 1957 | Version of ~ 19.41 with tw... |
| 19.41vvv 1958 | Version of ~ 19.41 with th... |
| 19.41vvvv 1959 | Version of ~ 19.41 with fo... |
| 19.42v 1960 | Version of ~ 19.42 with a ... |
| exdistr 1961 | Distribution of existentia... |
| exdistrv 1962 | Distribute a pair of exist... |
| 4exdistrv 1963 | Distribute two pairs of ex... |
| 19.42vv 1964 | Version of ~ 19.42 with tw... |
| exdistr2 1965 | Distribution of existentia... |
| 19.42vvv 1966 | Version of ~ 19.42 with th... |
| 3exdistr 1967 | Distribution of existentia... |
| 4exdistr 1968 | Distribution of existentia... |
| weq 1969 | Extend wff definition to i... |
| speimfw 1970 | Specialization, with addit... |
| speimfwALT 1971 | Alternate proof of ~ speim... |
| spimfw 1972 | Specialization, with addit... |
| ax12i 1973 | Inference that has ~ ax-12... |
| ax6v 1975 | Axiom B7 of [Tarski] p. 75... |
| ax6ev 1976 | At least one individual ex... |
| spimw 1977 | Specialization. Lemma 8 o... |
| spimew 1978 | Existential introduction, ... |
| spimehOLD 1979 | Obsolete version of ~ spim... |
| speiv 1980 | Inference from existential... |
| speivw 1981 | Version of ~ spei with a d... |
| exgen 1982 | Rule of existential genera... |
| exgenOLD 1983 | Obsolete version of ~ exge... |
| extru 1984 | There exists a variable su... |
| 19.2 1985 | Theorem 19.2 of [Margaris]... |
| 19.2d 1986 | Deduction associated with ... |
| 19.8w 1987 | Weak version of ~ 19.8a an... |
| spnfw 1988 | Weak version of ~ sp . Us... |
| spvw 1989 | Version of ~ sp when ` x `... |
| 19.3v 1990 | Version of ~ 19.3 with a d... |
| 19.8v 1991 | Version of ~ 19.8a with a ... |
| 19.9v 1992 | Version of ~ 19.9 with a d... |
| 19.3vOLD 1993 | Obsolete version of ~ 19.3... |
| spvwOLD 1994 | Obsolete version of ~ spvw... |
| 19.39 1995 | Theorem 19.39 of [Margaris... |
| 19.24 1996 | Theorem 19.24 of [Margaris... |
| 19.34 1997 | Theorem 19.34 of [Margaris... |
| 19.36v 1998 | Version of ~ 19.36 with a ... |
| 19.12vvv 1999 | Version of ~ 19.12vv with ... |
| 19.27v 2000 | Version of ~ 19.27 with a ... |
| 19.28v 2001 | Version of ~ 19.28 with a ... |
| 19.37v 2002 | Version of ~ 19.37 with a ... |
| 19.44v 2003 | Version of ~ 19.44 with a ... |
| 19.45v 2004 | Version of ~ 19.45 with a ... |
| spimevw 2005 | Existential introduction, ... |
| spimvw 2006 | A weak form of specializat... |
| spvv 2007 | Specialization, using impl... |
| spfalw 2008 | Version of ~ sp when ` ph ... |
| chvarvv 2009 | Implicit substitution of `... |
| equs4v 2010 | Version of ~ equs4 with a ... |
| alequexv 2011 | Version of ~ equs4v with i... |
| exsbim 2012 | One direction of the equiv... |
| equsv 2013 | If a formula does not cont... |
| equsalvw 2014 | Version of ~ equsalv with ... |
| equsexvw 2015 | Version of ~ equsexv with ... |
| equsexvwOLD 2016 | Obsolete version of ~ equs... |
| cbvaliw 2017 | Change bound variable. Us... |
| cbvalivw 2018 | Change bound variable. Us... |
| ax7v 2020 | Weakened version of ~ ax-7... |
| ax7v1 2021 | First of two weakened vers... |
| ax7v2 2022 | Second of two weakened ver... |
| equid 2023 | Identity law for equality.... |
| nfequid 2024 | Bound-variable hypothesis ... |
| equcomiv 2025 | Weaker form of ~ equcomi w... |
| ax6evr 2026 | A commuted form of ~ ax6ev... |
| ax7 2027 | Proof of ~ ax-7 from ~ ax7... |
| equcomi 2028 | Commutative law for equali... |
| equcom 2029 | Commutative law for equali... |
| equcomd 2030 | Deduction form of ~ equcom... |
| equcoms 2031 | An inference commuting equ... |
| equtr 2032 | A transitive law for equal... |
| equtrr 2033 | A transitive law for equal... |
| equeuclr 2034 | Commuted version of ~ eque... |
| equeucl 2035 | Equality is a left-Euclide... |
| equequ1 2036 | An equivalence law for equ... |
| equequ2 2037 | An equivalence law for equ... |
| equtr2 2038 | Equality is a left-Euclide... |
| stdpc6 2039 | One of the two equality ax... |
| equvinv 2040 | A variable introduction la... |
| equvinva 2041 | A modified version of the ... |
| equvelv 2042 | A biconditional form of ~ ... |
| ax13b 2043 | An equivalence between two... |
| spfw 2044 | Weak version of ~ sp . Us... |
| spw 2045 | Weak version of the specia... |
| cbvalw 2046 | Change bound variable. Us... |
| cbvalvw 2047 | Change bound variable. Us... |
| cbvexvw 2048 | Change bound variable. Us... |
| cbvaldvaw 2049 | Rule used to change the bo... |
| cbvexdvaw 2050 | Rule used to change the bo... |
| cbval2vw 2051 | Rule used to change bound ... |
| cbvex2vw 2052 | Rule used to change bound ... |
| cbvex4vw 2053 | Rule used to change bound ... |
| alcomiw 2054 | Weak version of ~ alcom . ... |
| alcomiwOLD 2055 | Obsolete version of ~ alco... |
| hbn1fw 2056 | Weak version of ~ ax-10 fr... |
| hbn1w 2057 | Weak version of ~ hbn1 . ... |
| hba1w 2058 | Weak version of ~ hba1 . ... |
| hbe1w 2059 | Weak version of ~ hbe1 . ... |
| hbalw 2060 | Weak version of ~ hbal . ... |
| spaev 2061 | A special instance of ~ sp... |
| cbvaev 2062 | Change bound variable in a... |
| aevlem0 2063 | Lemma for ~ aevlem . Inst... |
| aevlem 2064 | Lemma for ~ aev and ~ axc1... |
| aeveq 2065 | The antecedent ` A. x x = ... |
| aev 2066 | A "distinctor elimination"... |
| aev2 2067 | A version of ~ aev with tw... |
| hbaev 2068 | All variables are effectiv... |
| naev 2069 | If some set variables can ... |
| naev2 2070 | Generalization of ~ hbnaev... |
| hbnaev 2071 | Any variable is free in ` ... |
| sbjust 2072 | Justification theorem for ... |
| sbt 2075 | A substitution into a theo... |
| sbtru 2076 | The result of substituting... |
| stdpc4 2077 | The specialization axiom o... |
| sbtALT 2078 | Alternate proof of ~ sbt ,... |
| 2stdpc4 2079 | A double specialization us... |
| sbi1 2080 | Distribute substitution ov... |
| spsbim 2081 | Distribute substitution ov... |
| spsbbi 2082 | Biconditional property for... |
| sbimi 2083 | Distribute substitution ov... |
| sb2imi 2084 | Distribute substitution ov... |
| sbbii 2085 | Infer substitution into bo... |
| 2sbbii 2086 | Infer double substitution ... |
| sbimdv 2087 | Deduction substituting bot... |
| sbbidv 2088 | Deduction substituting bot... |
| sban 2089 | Conjunction inside and out... |
| sb3an 2090 | Threefold conjunction insi... |
| spsbe 2091 | Existential generalization... |
| sbequ 2092 | Equality property for subs... |
| sbequi 2093 | An equality theorem for su... |
| sb6 2094 | Alternate definition of su... |
| 2sb6 2095 | Equivalence for double sub... |
| sb1v 2096 | One direction of ~ sb5 , p... |
| sbv 2097 | Substitution for a variabl... |
| sbcom4 2098 | Commutativity law for subs... |
| pm11.07 2099 | Axiom *11.07 in [Whitehead... |
| sbrimvlem 2100 | Common proof template for ... |
| sbrimvw 2101 | Substitution in an implica... |
| sbievw 2102 | Conversion of implicit sub... |
| sbiedvw 2103 | Conversion of implicit sub... |
| 2sbievw 2104 | Conversion of double impli... |
| sbcom3vv 2105 | Substituting ` y ` for ` x... |
| sbievw2 2106 | ~ sbievw applied twice, av... |
| sbco2vv 2107 | A composition law for subs... |
| equsb3 2108 | Substitution in an equalit... |
| equsb3r 2109 | Substitution applied to th... |
| equsb1v 2110 | Substitution applied to an... |
| nsb 2111 | Any substitution in an alw... |
| sbn1 2112 | One direction of ~ sbn , u... |
| wel 2114 | Extend wff definition to i... |
| ax8v 2116 | Weakened version of ~ ax-8... |
| ax8v1 2117 | First of two weakened vers... |
| ax8v2 2118 | Second of two weakened ver... |
| ax8 2119 | Proof of ~ ax-8 from ~ ax8... |
| elequ1 2120 | An identity law for the no... |
| elsb3 2121 | Substitution applied to an... |
| cleljust 2122 | When the class variables i... |
| ax9v 2124 | Weakened version of ~ ax-9... |
| ax9v1 2125 | First of two weakened vers... |
| ax9v2 2126 | Second of two weakened ver... |
| ax9 2127 | Proof of ~ ax-9 from ~ ax9... |
| elequ2 2128 | An identity law for the no... |
| elsb4 2129 | Substitution applied to an... |
| elequ2g 2130 | A form of ~ elequ2 with a ... |
| ax6dgen 2131 | Tarski's system uses the w... |
| ax10w 2132 | Weak version of ~ ax-10 fr... |
| ax11w 2133 | Weak version of ~ ax-11 fr... |
| ax11dgen 2134 | Degenerate instance of ~ a... |
| ax12wlem 2135 | Lemma for weak version of ... |
| ax12w 2136 | Weak version of ~ ax-12 fr... |
| ax12dgen 2137 | Degenerate instance of ~ a... |
| ax12wdemo 2138 | Example of an application ... |
| ax13w 2139 | Weak version (principal in... |
| ax13dgen1 2140 | Degenerate instance of ~ a... |
| ax13dgen2 2141 | Degenerate instance of ~ a... |
| ax13dgen3 2142 | Degenerate instance of ~ a... |
| ax13dgen4 2143 | Degenerate instance of ~ a... |
| hbn1 2145 | Alias for ~ ax-10 to be us... |
| hbe1 2146 | The setvar ` x ` is not fr... |
| hbe1a 2147 | Dual statement of ~ hbe1 .... |
| nf5-1 2148 | One direction of ~ nf5 can... |
| nf5i 2149 | Deduce that ` x ` is not f... |
| nf5dh 2150 | Deduce that ` x ` is not f... |
| nf5dv 2151 | Apply the definition of no... |
| nfnaew 2152 | All variables are effectiv... |
| nfnaewOLD 2153 | Obsolete version of ~ nfna... |
| nfe1 2154 | The setvar ` x ` is not fr... |
| nfa1 2155 | The setvar ` x ` is not fr... |
| nfna1 2156 | A convenience theorem part... |
| nfia1 2157 | Lemma 23 of [Monk2] p. 114... |
| nfnf1 2158 | The setvar ` x ` is not fr... |
| modal5 2159 | The analogue in our predic... |
| nfs1v 2160 | The setvar ` x ` is not fr... |
| alcoms 2162 | Swap quantifiers in an ant... |
| alcom 2163 | Theorem 19.5 of [Margaris]... |
| alrot3 2164 | Theorem *11.21 in [Whitehe... |
| alrot4 2165 | Rotate four universal quan... |
| sbal 2166 | Move universal quantifier ... |
| sbalv 2167 | Quantify with new variable... |
| sbcom2 2168 | Commutativity law for subs... |
| excom 2169 | Theorem 19.11 of [Margaris... |
| excomim 2170 | One direction of Theorem 1... |
| excom13 2171 | Swap 1st and 3rd existenti... |
| exrot3 2172 | Rotate existential quantif... |
| exrot4 2173 | Rotate existential quantif... |
| hbal 2174 | If ` x ` is not free in ` ... |
| hbald 2175 | Deduction form of bound-va... |
| hbsbw 2176 | If ` z ` is not free in ` ... |
| nfa2 2177 | Lemma 24 of [Monk2] p. 114... |
| ax12v 2179 | This is essentially Axiom ... |
| ax12v2 2180 | It is possible to remove a... |
| 19.8a 2181 | If a wff is true, it is tr... |
| 19.8ad 2182 | If a wff is true, it is tr... |
| sp 2183 | Specialization. A univers... |
| spi 2184 | Inference rule of universa... |
| sps 2185 | Generalization of antecede... |
| 2sp 2186 | A double specialization (s... |
| spsd 2187 | Deduction generalizing ant... |
| 19.2g 2188 | Theorem 19.2 of [Margaris]... |
| 19.21bi 2189 | Inference form of ~ 19.21 ... |
| 19.21bbi 2190 | Inference removing two uni... |
| 19.23bi 2191 | Inference form of Theorem ... |
| nexr 2192 | Inference associated with ... |
| qexmid 2193 | Quantified excluded middle... |
| nf5r 2194 | Consequence of the definit... |
| nf5rOLD 2195 | Obsolete version of ~ nfrd... |
| nf5ri 2196 | Consequence of the definit... |
| nf5rd 2197 | Consequence of the definit... |
| spimedv 2198 | Deduction version of ~ spi... |
| spimefv 2199 | Version of ~ spime with a ... |
| nfim1 2200 | A closed form of ~ nfim . ... |
| nfan1 2201 | A closed form of ~ nfan . ... |
| 19.3t 2202 | Closed form of ~ 19.3 and ... |
| 19.3 2203 | A wff may be quantified wi... |
| 19.9d 2204 | A deduction version of one... |
| 19.9t 2205 | Closed form of ~ 19.9 and ... |
| 19.9 2206 | A wff may be existentially... |
| 19.21t 2207 | Closed form of Theorem 19.... |
| 19.21 2208 | Theorem 19.21 of [Margaris... |
| stdpc5 2209 | An axiom scheme of standar... |
| 19.21-2 2210 | Version of ~ 19.21 with tw... |
| 19.23t 2211 | Closed form of Theorem 19.... |
| 19.23 2212 | Theorem 19.23 of [Margaris... |
| alimd 2213 | Deduction form of Theorem ... |
| alrimi 2214 | Inference form of Theorem ... |
| alrimdd 2215 | Deduction form of Theorem ... |
| alrimd 2216 | Deduction form of Theorem ... |
| eximd 2217 | Deduction form of Theorem ... |
| exlimi 2218 | Inference associated with ... |
| exlimd 2219 | Deduction form of Theorem ... |
| exlimimdd 2220 | Existential elimination ru... |
| exlimdd 2221 | Existential elimination ru... |
| nexd 2222 | Deduction for generalizati... |
| albid 2223 | Formula-building rule for ... |
| exbid 2224 | Formula-building rule for ... |
| nfbidf 2225 | An equality theorem for ef... |
| 19.16 2226 | Theorem 19.16 of [Margaris... |
| 19.17 2227 | Theorem 19.17 of [Margaris... |
| 19.27 2228 | Theorem 19.27 of [Margaris... |
| 19.28 2229 | Theorem 19.28 of [Margaris... |
| 19.19 2230 | Theorem 19.19 of [Margaris... |
| 19.36 2231 | Theorem 19.36 of [Margaris... |
| 19.36i 2232 | Inference associated with ... |
| 19.37 2233 | Theorem 19.37 of [Margaris... |
| 19.32 2234 | Theorem 19.32 of [Margaris... |
| 19.31 2235 | Theorem 19.31 of [Margaris... |
| 19.41 2236 | Theorem 19.41 of [Margaris... |
| 19.42 2237 | Theorem 19.42 of [Margaris... |
| 19.44 2238 | Theorem 19.44 of [Margaris... |
| 19.45 2239 | Theorem 19.45 of [Margaris... |
| spimfv 2240 | Specialization, using impl... |
| chvarfv 2241 | Implicit substitution of `... |
| cbv3v2 2242 | Version of ~ cbv3 with two... |
| sbalex 2243 | Equivalence of two ways to... |
| sb4av 2244 | Version of ~ sb4a with a d... |
| sbimd 2245 | Deduction substituting bot... |
| sbbid 2246 | Deduction substituting bot... |
| 2sbbid 2247 | Deduction doubly substitut... |
| sbequ1 2248 | An equality theorem for su... |
| sbequ2 2249 | An equality theorem for su... |
| sbequ2OLD 2250 | Obsolete version of ~ sbeq... |
| stdpc7 2251 | One of the two equality ax... |
| sbequ12 2252 | An equality theorem for su... |
| sbequ12r 2253 | An equality theorem for su... |
| sbelx 2254 | Elimination of substitutio... |
| sbequ12a 2255 | An equality theorem for su... |
| sbid 2256 | An identity theorem for su... |
| sbcov 2257 | A composition law for subs... |
| sb6a 2258 | Equivalence for substituti... |
| sbid2vw 2259 | Reverting substitution yie... |
| axc16g 2260 | Generalization of ~ axc16 ... |
| axc16 2261 | Proof of older axiom ~ ax-... |
| axc16gb 2262 | Biconditional strengthenin... |
| axc16nf 2263 | If ~ dtru is false, then t... |
| axc11v 2264 | Version of ~ axc11 with a ... |
| axc11rv 2265 | Version of ~ axc11r with a... |
| drsb2 2266 | Formula-building lemma for... |
| equsalv 2267 | An equivalence related to ... |
| equsexv 2268 | An equivalence related to ... |
| sbft 2269 | Substitution has no effect... |
| sbf 2270 | Substitution for a variabl... |
| sbf2 2271 | Substitution has no effect... |
| sbh 2272 | Substitution for a variabl... |
| hbs1 2273 | The setvar ` x ` is not fr... |
| nfs1f 2274 | If ` x ` is not free in ` ... |
| sb5 2275 | Alternate definition of su... |
| sb5OLD 2276 | Obsolete version of ~ sb5 ... |
| sb56OLD 2277 | Obsolete version of ~ sbal... |
| equs5av 2278 | A property related to subs... |
| 2sb5 2279 | Equivalence for double sub... |
| sbco4lem 2280 | Lemma for ~ sbco4 . It re... |
| sbco4 2281 | Two ways of exchanging two... |
| dfsb7 2282 | An alternate definition of... |
| sbn 2283 | Negation inside and outsid... |
| sbex 2284 | Move existential quantifie... |
| nf5 2285 | Alternate definition of ~ ... |
| nf6 2286 | An alternate definition of... |
| nf5d 2287 | Deduce that ` x ` is not f... |
| nf5di 2288 | Since the converse holds b... |
| 19.9h 2289 | A wff may be existentially... |
| 19.21h 2290 | Theorem 19.21 of [Margaris... |
| 19.23h 2291 | Theorem 19.23 of [Margaris... |
| exlimih 2292 | Inference associated with ... |
| exlimdh 2293 | Deduction form of Theorem ... |
| equsalhw 2294 | Version of ~ equsalh with ... |
| equsexhv 2295 | An equivalence related to ... |
| hba1 2296 | The setvar ` x ` is not fr... |
| hbnt 2297 | Closed theorem version of ... |
| hbn 2298 | If ` x ` is not free in ` ... |
| hbnd 2299 | Deduction form of bound-va... |
| hbim1 2300 | A closed form of ~ hbim . ... |
| hbimd 2301 | Deduction form of bound-va... |
| hbim 2302 | If ` x ` is not free in ` ... |
| hban 2303 | If ` x ` is not free in ` ... |
| hb3an 2304 | If ` x ` is not free in ` ... |
| sbi2 2305 | Introduction of implicatio... |
| sbim 2306 | Implication inside and out... |
| sbrim 2307 | Substitution in an implica... |
| sbrimv 2308 | Substitution in an implica... |
| sblim 2309 | Substitution in an implica... |
| sbor 2310 | Disjunction inside and out... |
| sbbi 2311 | Equivalence inside and out... |
| sblbis 2312 | Introduce left bicondition... |
| sbrbis 2313 | Introduce right biconditio... |
| sbrbif 2314 | Introduce right biconditio... |
| sbiev 2315 | Conversion of implicit sub... |
| sbiedw 2316 | Conversion of implicit sub... |
| sbiedwOLD 2317 | Obsolete version of ~ sbie... |
| axc7 2318 | Show that the original axi... |
| axc7e 2319 | Abbreviated version of ~ a... |
| modal-b 2320 | The analogue in our predic... |
| 19.9ht 2321 | A closed version of ~ 19.9... |
| axc4 2322 | Show that the original axi... |
| axc4i 2323 | Inference version of ~ axc... |
| nfal 2324 | If ` x ` is not free in ` ... |
| nfex 2325 | If ` x ` is not free in ` ... |
| hbex 2326 | If ` x ` is not free in ` ... |
| nfnf 2327 | If ` x ` is not free in ` ... |
| 19.12 2328 | Theorem 19.12 of [Margaris... |
| nfald 2329 | Deduction form of ~ nfal .... |
| nfexd 2330 | If ` x ` is not free in ` ... |
| nfsbv 2331 | If ` z ` is not free in ` ... |
| hbsbwOLD 2332 | Obsolete version of ~ hbsb... |
| sbco2v 2333 | A composition law for subs... |
| aaan 2334 | Rearrange universal quanti... |
| eeor 2335 | Rearrange existential quan... |
| cbv3v 2336 | Rule used to change bound ... |
| cbv1v 2337 | Rule used to change bound ... |
| cbv2w 2338 | Rule used to change bound ... |
| cbvaldw 2339 | Deduction used to change b... |
| cbvexdw 2340 | Deduction used to change b... |
| cbv3hv 2341 | Rule used to change bound ... |
| cbvalv1 2342 | Rule used to change bound ... |
| cbvexv1 2343 | Rule used to change bound ... |
| cbval2v 2344 | Rule used to change bound ... |
| cbval2vOLD 2345 | Obsolete version of ~ cbva... |
| cbvex2v 2346 | Rule used to change bound ... |
| dvelimhw 2347 | Proof of ~ dvelimh without... |
| pm11.53 2348 | Theorem *11.53 in [Whitehe... |
| 19.12vv 2349 | Special case of ~ 19.12 wh... |
| eean 2350 | Rearrange existential quan... |
| eeanv 2351 | Distribute a pair of exist... |
| eeeanv 2352 | Distribute three existenti... |
| ee4anv 2353 | Distribute two pairs of ex... |
| sb8v 2354 | Substitution of variable i... |
| sb8ev 2355 | Substitution of variable i... |
| 2sb8ev 2356 | An equivalent expression f... |
| sb6rfv 2357 | Reversed substitution. Ve... |
| sbnf2 2358 | Two ways of expressing " `... |
| exsb 2359 | An equivalent expression f... |
| 2exsb 2360 | An equivalent expression f... |
| sbbib 2361 | Reversal of substitution. ... |
| sbbibvv 2362 | Reversal of substitution. ... |
| cleljustALT 2363 | Alternate proof of ~ clelj... |
| cleljustALT2 2364 | Alternate proof of ~ clelj... |
| equs5aALT 2365 | Alternate proof of ~ equs5... |
| equs5eALT 2366 | Alternate proof of ~ equs5... |
| axc11r 2367 | Same as ~ axc11 but with r... |
| dral1v 2368 | Formula-building lemma for... |
| drex1v 2369 | Formula-building lemma for... |
| drnf1v 2370 | Formula-building lemma for... |
| ax13v 2372 | A weaker version of ~ ax-1... |
| ax13lem1 2373 | A version of ~ ax13v with ... |
| ax13 2374 | Derive ~ ax-13 from ~ ax13... |
| ax13lem2 2375 | Lemma for ~ nfeqf2 . This... |
| nfeqf2 2376 | An equation between setvar... |
| dveeq2 2377 | Quantifier introduction wh... |
| nfeqf1 2378 | An equation between setvar... |
| dveeq1 2379 | Quantifier introduction wh... |
| nfeqf 2380 | A variable is effectively ... |
| axc9 2381 | Derive set.mm's original ~... |
| ax6e 2382 | At least one individual ex... |
| ax6 2383 | Theorem showing that ~ ax-... |
| axc10 2384 | Show that the original axi... |
| spimt 2385 | Closed theorem form of ~ s... |
| spim 2386 | Specialization, using impl... |
| spimed 2387 | Deduction version of ~ spi... |
| spime 2388 | Existential introduction, ... |
| spimv 2389 | A version of ~ spim with a... |
| spimvALT 2390 | Alternate proof of ~ spimv... |
| spimev 2391 | Distinct-variable version ... |
| spv 2392 | Specialization, using impl... |
| spei 2393 | Inference from existential... |
| chvar 2394 | Implicit substitution of `... |
| chvarv 2395 | Implicit substitution of `... |
| cbv3 2396 | Rule used to change bound ... |
| cbval 2397 | Rule used to change bound ... |
| cbvex 2398 | Rule used to change bound ... |
| cbvalv 2399 | Rule used to change bound ... |
| cbvexv 2400 | Rule used to change bound ... |
| cbv1 2401 | Rule used to change bound ... |
| cbv2 2402 | Rule used to change bound ... |
| cbv3h 2403 | Rule used to change bound ... |
| cbv1h 2404 | Rule used to change bound ... |
| cbv2h 2405 | Rule used to change bound ... |
| cbvald 2406 | Deduction used to change b... |
| cbvexd 2407 | Deduction used to change b... |
| cbvaldva 2408 | Rule used to change the bo... |
| cbvexdva 2409 | Rule used to change the bo... |
| cbval2 2410 | Rule used to change bound ... |
| cbvex2 2411 | Rule used to change bound ... |
| cbval2vv 2412 | Rule used to change bound ... |
| cbvex2vv 2413 | Rule used to change bound ... |
| cbvex4v 2414 | Rule used to change bound ... |
| equs4 2415 | Lemma used in proofs of im... |
| equsal 2416 | An equivalence related to ... |
| equsex 2417 | An equivalence related to ... |
| equsexALT 2418 | Alternate proof of ~ equse... |
| equsalh 2419 | An equivalence related to ... |
| equsexh 2420 | An equivalence related to ... |
| axc15 2421 | Derivation of set.mm's ori... |
| ax12 2422 | Rederivation of Axiom ~ ax... |
| ax12b 2423 | A bidirectional version of... |
| ax13ALT 2424 | Alternate proof of ~ ax13 ... |
| axc11n 2425 | Derive set.mm's original ~... |
| aecom 2426 | Commutation law for identi... |
| aecoms 2427 | A commutation rule for ide... |
| naecoms 2428 | A commutation rule for dis... |
| axc11 2429 | Show that ~ ax-c11 can be ... |
| hbae 2430 | All variables are effectiv... |
| hbnae 2431 | All variables are effectiv... |
| nfae 2432 | All variables are effectiv... |
| nfnae 2433 | All variables are effectiv... |
| hbnaes 2434 | Rule that applies ~ hbnae ... |
| axc16i 2435 | Inference with ~ axc16 as ... |
| axc16nfALT 2436 | Alternate proof of ~ axc16... |
| dral2 2437 | Formula-building lemma for... |
| dral1 2438 | Formula-building lemma for... |
| dral1ALT 2439 | Alternate proof of ~ dral1... |
| drex1 2440 | Formula-building lemma for... |
| drex2 2441 | Formula-building lemma for... |
| drnf1 2442 | Formula-building lemma for... |
| drnf2 2443 | Formula-building lemma for... |
| nfald2 2444 | Variation on ~ nfald which... |
| nfexd2 2445 | Variation on ~ nfexd which... |
| exdistrf 2446 | Distribution of existentia... |
| dvelimf 2447 | Version of ~ dvelimv witho... |
| dvelimdf 2448 | Deduction form of ~ dvelim... |
| dvelimh 2449 | Version of ~ dvelim withou... |
| dvelim 2450 | This theorem can be used t... |
| dvelimv 2451 | Similar to ~ dvelim with f... |
| dvelimnf 2452 | Version of ~ dvelim using ... |
| dveeq2ALT 2453 | Alternate proof of ~ dveeq... |
| equvini 2454 | A variable introduction la... |
| equvel 2455 | A variable elimination law... |
| equs5a 2456 | A property related to subs... |
| equs5e 2457 | A property related to subs... |
| equs45f 2458 | Two ways of expressing sub... |
| equs5 2459 | Lemma used in proofs of su... |
| dveel1 2460 | Quantifier introduction wh... |
| dveel2 2461 | Quantifier introduction wh... |
| axc14 2462 | Axiom ~ ax-c14 is redundan... |
| sb6x 2463 | Equivalence involving subs... |
| sbequ5 2464 | Substitution does not chan... |
| sbequ6 2465 | Substitution does not chan... |
| sb5rf 2466 | Reversed substitution. Us... |
| sb6rf 2467 | Reversed substitution. Fo... |
| ax12vALT 2468 | Alternate proof of ~ ax12v... |
| 2ax6elem 2469 | We can always find values ... |
| 2ax6e 2470 | We can always find values ... |
| 2ax6eOLD 2471 | Obsolete version of ~ 2ax6... |
| 2sb5rf 2472 | Reversed double substituti... |
| 2sb6rf 2473 | Reversed double substituti... |
| sbel2x 2474 | Elimination of double subs... |
| sb4b 2475 | Simplified definition of s... |
| sb4bOLD 2476 | Obsolete version of ~ sb4b... |
| sb3b 2477 | Simplified definition of s... |
| sb3 2478 | One direction of a simplif... |
| sb1 2479 | One direction of a simplif... |
| sb2 2480 | One direction of a simplif... |
| sb3OLD 2481 | Obsolete version of ~ sb3 ... |
| sb1OLD 2482 | Obsolete version of ~ sb1 ... |
| sb3bOLD 2483 | Obsolete version of ~ sb3b... |
| sb4a 2484 | A version of one implicati... |
| dfsb1 2485 | Alternate definition of su... |
| hbsb2 2486 | Bound-variable hypothesis ... |
| nfsb2 2487 | Bound-variable hypothesis ... |
| hbsb2a 2488 | Special case of a bound-va... |
| sb4e 2489 | One direction of a simplif... |
| hbsb2e 2490 | Special case of a bound-va... |
| hbsb3 2491 | If ` y ` is not free in ` ... |
| nfs1 2492 | If ` y ` is not free in ` ... |
| axc16ALT 2493 | Alternate proof of ~ axc16... |
| axc16gALT 2494 | Alternate proof of ~ axc16... |
| equsb1 2495 | Substitution applied to an... |
| equsb2 2496 | Substitution applied to an... |
| dfsb2 2497 | An alternate definition of... |
| dfsb3 2498 | An alternate definition of... |
| drsb1 2499 | Formula-building lemma for... |
| sb2ae 2500 | In the case of two success... |
| sb6f 2501 | Equivalence for substituti... |
| sb5f 2502 | Equivalence for substituti... |
| nfsb4t 2503 | A variable not free in a p... |
| nfsb4 2504 | A variable not free in a p... |
| sbequ8 2505 | Elimination of equality fr... |
| sbie 2506 | Conversion of implicit sub... |
| sbied 2507 | Conversion of implicit sub... |
| sbiedv 2508 | Conversion of implicit sub... |
| 2sbiev 2509 | Conversion of double impli... |
| sbcom3 2510 | Substituting ` y ` for ` x... |
| sbco 2511 | A composition law for subs... |
| sbid2 2512 | An identity law for substi... |
| sbid2v 2513 | An identity law for substi... |
| sbidm 2514 | An idempotent law for subs... |
| sbco2 2515 | A composition law for subs... |
| sbco2d 2516 | A composition law for subs... |
| sbco3 2517 | A composition law for subs... |
| sbcom 2518 | A commutativity law for su... |
| sbtrt 2519 | Partially closed form of ~... |
| sbtr 2520 | A partial converse to ~ sb... |
| sb8 2521 | Substitution of variable i... |
| sb8e 2522 | Substitution of variable i... |
| sb9 2523 | Commutation of quantificat... |
| sb9i 2524 | Commutation of quantificat... |
| sbhb 2525 | Two ways of expressing " `... |
| nfsbd 2526 | Deduction version of ~ nfs... |
| nfsb 2527 | If ` z ` is not free in ` ... |
| nfsbOLD 2528 | Obsolete version of ~ nfsb... |
| hbsb 2529 | If ` z ` is not free in ` ... |
| sb7f 2530 | This version of ~ dfsb7 do... |
| sb7h 2531 | This version of ~ dfsb7 do... |
| sb10f 2532 | Hao Wang's identity axiom ... |
| sbal1 2533 | Check out ~ sbal for a ver... |
| sbal2 2534 | Move quantifier in and out... |
| 2sb8e 2535 | An equivalent expression f... |
| dfmoeu 2536 | An elementary proof of ~ m... |
| dfeumo 2537 | An elementary proof showin... |
| mojust 2539 | Soundness justification th... |
| nexmo 2541 | Nonexistence implies uniqu... |
| exmo 2542 | Any proposition holds for ... |
| moabs 2543 | Absorption of existence co... |
| moim 2544 | The at-most-one quantifier... |
| moimi 2545 | The at-most-one quantifier... |
| moimdv 2546 | The at-most-one quantifier... |
| mobi 2547 | Equivalence theorem for th... |
| mobii 2548 | Formula-building rule for ... |
| mobidv 2549 | Formula-building rule for ... |
| mobid 2550 | Formula-building rule for ... |
| moa1 2551 | If an implication holds fo... |
| moan 2552 | "At most one" is still the... |
| moani 2553 | "At most one" is still tru... |
| moor 2554 | "At most one" is still the... |
| mooran1 2555 | "At most one" imports disj... |
| mooran2 2556 | "At most one" exports disj... |
| nfmo1 2557 | Bound-variable hypothesis ... |
| nfmod2 2558 | Bound-variable hypothesis ... |
| nfmodv 2559 | Bound-variable hypothesis ... |
| nfmov 2560 | Bound-variable hypothesis ... |
| nfmod 2561 | Bound-variable hypothesis ... |
| nfmo 2562 | Bound-variable hypothesis ... |
| mof 2563 | Version of ~ df-mo with di... |
| mo3 2564 | Alternate definition of th... |
| mo 2565 | Equivalent definitions of ... |
| mo4 2566 | At-most-one quantifier exp... |
| mo4f 2567 | At-most-one quantifier exp... |
| mo4OLD 2568 | Obsolete version of ~ mo4 ... |
| eu3v 2571 | An alternate way to expres... |
| eujust 2572 | Soundness justification th... |
| eujustALT 2573 | Alternate proof of ~ eujus... |
| eu6lem 2574 | Lemma of ~ eu6im . A diss... |
| eu6 2575 | Alternate definition of th... |
| eu6im 2576 | One direction of ~ eu6 nee... |
| euf 2577 | Version of ~ eu6 with disj... |
| euex 2578 | Existential uniqueness imp... |
| eumo 2579 | Existential uniqueness imp... |
| eumoi 2580 | Uniqueness inferred from e... |
| exmoeub 2581 | Existence implies that uni... |
| exmoeu 2582 | Existence is equivalent to... |
| moeuex 2583 | Uniqueness implies that ex... |
| moeu 2584 | Uniqueness is equivalent t... |
| eubi 2585 | Equivalence theorem for th... |
| eubii 2586 | Introduce unique existenti... |
| eubidv 2587 | Formula-building rule for ... |
| eubid 2588 | Formula-building rule for ... |
| nfeu1 2589 | Bound-variable hypothesis ... |
| nfeu1ALT 2590 | Alternate proof of ~ nfeu1... |
| nfeud2 2591 | Bound-variable hypothesis ... |
| nfeudw 2592 | Bound-variable hypothesis ... |
| nfeud 2593 | Bound-variable hypothesis ... |
| nfeuw 2594 | Bound-variable hypothesis ... |
| nfeu 2595 | Bound-variable hypothesis ... |
| dfeu 2596 | Rederive ~ df-eu from the ... |
| dfmo 2597 | Rederive ~ df-mo from the ... |
| euequ 2598 | There exists a unique set ... |
| sb8eulem 2599 | Lemma. Factor out the com... |
| sb8euv 2600 | Variable substitution in u... |
| sb8eu 2601 | Variable substitution in u... |
| sb8mo 2602 | Variable substitution for ... |
| cbvmovw 2603 | Change bound variable. Us... |
| cbvmow 2604 | Rule used to change bound ... |
| cbvmowOLD 2605 | Obsolete version of ~ cbvm... |
| cbvmo 2606 | Rule used to change bound ... |
| cbveuvw 2607 | Change bound variable. Us... |
| cbveuw 2608 | Version of ~ cbveu with a ... |
| cbveuwOLD 2609 | Obsolete version of ~ cbve... |
| cbveu 2610 | Rule used to change bound ... |
| cbveuALT 2611 | Alternative proof of ~ cbv... |
| eu2 2612 | An alternate way of defini... |
| eu1 2613 | An alternate way to expres... |
| euor 2614 | Introduce a disjunct into ... |
| euorv 2615 | Introduce a disjunct into ... |
| euor2 2616 | Introduce or eliminate a d... |
| sbmo 2617 | Substitution into an at-mo... |
| eu4 2618 | Uniqueness using implicit ... |
| euimmo 2619 | Existential uniqueness imp... |
| euim 2620 | Add unique existential qua... |
| moanimlem 2621 | Factor out the common proo... |
| moanimv 2622 | Introduction of a conjunct... |
| moanim 2623 | Introduction of a conjunct... |
| euan 2624 | Introduction of a conjunct... |
| moanmo 2625 | Nested at-most-one quantif... |
| moaneu 2626 | Nested at-most-one and uni... |
| euanv 2627 | Introduction of a conjunct... |
| mopick 2628 | "At most one" picks a vari... |
| moexexlem 2629 | Factor out the proof skele... |
| 2moexv 2630 | Double quantification with... |
| moexexvw 2631 | "At most one" double quant... |
| 2moswapv 2632 | A condition allowing to sw... |
| 2euswapv 2633 | A condition allowing to sw... |
| 2euexv 2634 | Double quantification with... |
| 2exeuv 2635 | Double existential uniquen... |
| eupick 2636 | Existential uniqueness "pi... |
| eupicka 2637 | Version of ~ eupick with c... |
| eupickb 2638 | Existential uniqueness "pi... |
| eupickbi 2639 | Theorem *14.26 in [Whitehe... |
| mopick2 2640 | "At most one" can show the... |
| moexex 2641 | "At most one" double quant... |
| moexexv 2642 | "At most one" double quant... |
| 2moex 2643 | Double quantification with... |
| 2euex 2644 | Double quantification with... |
| 2eumo 2645 | Nested unique existential ... |
| 2eu2ex 2646 | Double existential uniquen... |
| 2moswap 2647 | A condition allowing to sw... |
| 2euswap 2648 | A condition allowing to sw... |
| 2exeu 2649 | Double existential uniquen... |
| 2mo2 2650 | Two ways of expressing "th... |
| 2mo 2651 | Two ways of expressing "th... |
| 2mos 2652 | Double "there exists at mo... |
| 2eu1 2653 | Double existential uniquen... |
| 2eu1v 2654 | Double existential uniquen... |
| 2eu2 2655 | Double existential uniquen... |
| 2eu3 2656 | Double existential uniquen... |
| 2eu4 2657 | This theorem provides us w... |
| 2eu5 2658 | An alternate definition of... |
| 2eu6 2659 | Two equivalent expressions... |
| 2eu7 2660 | Two equivalent expressions... |
| 2eu8 2661 | Two equivalent expressions... |
| euae 2662 | Two ways to express "exact... |
| exists1 2663 | Two ways to express "exact... |
| exists2 2664 | A condition implying that ... |
| barbara 2665 | "Barbara", one of the fund... |
| celarent 2666 | "Celarent", one of the syl... |
| darii 2667 | "Darii", one of the syllog... |
| dariiALT 2668 | Alternate proof of ~ darii... |
| ferio 2669 | "Ferio" ("Ferioque"), one ... |
| barbarilem 2670 | Lemma for ~ barbari and th... |
| barbari 2671 | "Barbari", one of the syll... |
| barbariALT 2672 | Alternate proof of ~ barba... |
| celaront 2673 | "Celaront", one of the syl... |
| cesare 2674 | "Cesare", one of the syllo... |
| camestres 2675 | "Camestres", one of the sy... |
| festino 2676 | "Festino", one of the syll... |
| festinoALT 2677 | Alternate proof of ~ festi... |
| baroco 2678 | "Baroco", one of the syllo... |
| barocoALT 2679 | Alternate proof of ~ festi... |
| cesaro 2680 | "Cesaro", one of the syllo... |
| camestros 2681 | "Camestros", one of the sy... |
| datisi 2682 | "Datisi", one of the syllo... |
| disamis 2683 | "Disamis", one of the syll... |
| ferison 2684 | "Ferison", one of the syll... |
| bocardo 2685 | "Bocardo", one of the syll... |
| darapti 2686 | "Darapti", one of the syll... |
| daraptiALT 2687 | Alternate proof of ~ darap... |
| felapton 2688 | "Felapton", one of the syl... |
| calemes 2689 | "Calemes", one of the syll... |
| dimatis 2690 | "Dimatis", one of the syll... |
| fresison 2691 | "Fresison", one of the syl... |
| calemos 2692 | "Calemos", one of the syll... |
| fesapo 2693 | "Fesapo", one of the syllo... |
| bamalip 2694 | "Bamalip", one of the syll... |
| axia1 2695 | Left 'and' elimination (in... |
| axia2 2696 | Right 'and' elimination (i... |
| axia3 2697 | 'And' introduction (intuit... |
| axin1 2698 | 'Not' introduction (intuit... |
| axin2 2699 | 'Not' elimination (intuiti... |
| axio 2700 | Definition of 'or' (intuit... |
| axi4 2701 | Specialization (intuitioni... |
| axi5r 2702 | Converse of ~ axc4 (intuit... |
| axial 2703 | The setvar ` x ` is not fr... |
| axie1 2704 | The setvar ` x ` is not fr... |
| axie2 2705 | A key property of existent... |
| axi9 2706 | Axiom of existence (intuit... |
| axi10 2707 | Axiom of Quantifier Substi... |
| axi12 2708 | Axiom of Quantifier Introd... |
| axbnd 2709 | Axiom of Bundling (intuiti... |
| axexte 2711 | The axiom of extensionalit... |
| axextg 2712 | A generalization of the ax... |
| axextb 2713 | A bidirectional version of... |
| axextmo 2714 | There exists at most one s... |
| nulmo 2715 | There exists at most one e... |
| eleq1ab 2718 | Extension (in the sense of... |
| cleljustab 2719 | Extension of ~ cleljust fr... |
| abid 2720 | Simplification of class ab... |
| vexwt 2721 | A standard theorem of pred... |
| vexw 2722 | If ` ph ` is a theorem, th... |
| vextru 2723 | Every setvar is a member o... |
| hbab1 2724 | Bound-variable hypothesis ... |
| nfsab1 2725 | Bound-variable hypothesis ... |
| hbab 2726 | Bound-variable hypothesis ... |
| hbabg 2727 | Bound-variable hypothesis ... |
| nfsab 2728 | Bound-variable hypothesis ... |
| nfsabg 2729 | Bound-variable hypothesis ... |
| dfcleq 2731 | The defining characterizat... |
| cvjust 2732 | Every set is a class. Pro... |
| ax9ALT 2733 | Proof of ~ ax-9 from Tarsk... |
| eleq2w2 2734 | A weaker version of ~ eleq... |
| eqriv 2735 | Infer equality of classes ... |
| eqrdv 2736 | Deduce equality of classes... |
| eqrdav 2737 | Deduce equality of classes... |
| eqid 2738 | Law of identity (reflexivi... |
| eqidd 2739 | Class identity law with an... |
| eqeq1d 2740 | Deduction from equality to... |
| eqeq1dALT 2741 | Shorter proof of ~ eqeq1d ... |
| eqeq1 2742 | Equality implies equivalen... |
| eqeq1i 2743 | Inference from equality to... |
| eqcomd 2744 | Deduction from commutative... |
| eqcom 2745 | Commutative law for class ... |
| eqcoms 2746 | Inference applying commuta... |
| eqcomi 2747 | Inference from commutative... |
| neqcomd 2748 | Commute an inequality. (C... |
| eqeq2d 2749 | Deduction from equality to... |
| eqeq2 2750 | Equality implies equivalen... |
| eqeq2i 2751 | Inference from equality to... |
| eqeq12 2752 | Equality relationship amon... |
| eqeq12i 2753 | A useful inference for sub... |
| eqeq12d 2754 | A useful inference for sub... |
| eqeqan12d 2755 | A useful inference for sub... |
| eqeqan12dALT 2756 | Alternate proof of ~ eqeqa... |
| eqeqan12rd 2757 | A useful inference for sub... |
| eqtr 2758 | Transitive law for class e... |
| eqtr2 2759 | A transitive law for class... |
| eqtr3 2760 | A transitive law for class... |
| eqtri 2761 | An equality transitivity i... |
| eqtr2i 2762 | An equality transitivity i... |
| eqtr3i 2763 | An equality transitivity i... |
| eqtr4i 2764 | An equality transitivity i... |
| 3eqtri 2765 | An inference from three ch... |
| 3eqtrri 2766 | An inference from three ch... |
| 3eqtr2i 2767 | An inference from three ch... |
| 3eqtr2ri 2768 | An inference from three ch... |
| 3eqtr3i 2769 | An inference from three ch... |
| 3eqtr3ri 2770 | An inference from three ch... |
| 3eqtr4i 2771 | An inference from three ch... |
| 3eqtr4ri 2772 | An inference from three ch... |
| eqtrd 2773 | An equality transitivity d... |
| eqtr2d 2774 | An equality transitivity d... |
| eqtr3d 2775 | An equality transitivity e... |
| eqtr4d 2776 | An equality transitivity e... |
| 3eqtrd 2777 | A deduction from three cha... |
| 3eqtrrd 2778 | A deduction from three cha... |
| 3eqtr2d 2779 | A deduction from three cha... |
| 3eqtr2rd 2780 | A deduction from three cha... |
| 3eqtr3d 2781 | A deduction from three cha... |
| 3eqtr3rd 2782 | A deduction from three cha... |
| 3eqtr4d 2783 | A deduction from three cha... |
| 3eqtr4rd 2784 | A deduction from three cha... |
| syl5eq 2785 | An equality transitivity d... |
| eqtr2id 2786 | An equality transitivity d... |
| eqtr3id 2787 | An equality transitivity d... |
| syl5reqr 2788 | An equality transitivity d... |
| eqtrdi 2789 | An equality transitivity d... |
| eqtr2di 2790 | An equality transitivity d... |
| eqtr4di 2791 | An equality transitivity d... |
| eqtr4id 2792 | An equality transitivity d... |
| sylan9eq 2793 | An equality transitivity d... |
| sylan9req 2794 | An equality transitivity d... |
| sylan9eqr 2795 | An equality transitivity d... |
| 3eqtr3g 2796 | A chained equality inferen... |
| 3eqtr3a 2797 | A chained equality inferen... |
| 3eqtr4g 2798 | A chained equality inferen... |
| 3eqtr4a 2799 | A chained equality inferen... |
| eq2tri 2800 | A compound transitive infe... |
| abbi1 2801 | Equivalent formulas yield ... |
| abbidv 2802 | Equivalent wff's yield equ... |
| abbii 2803 | Equivalent wff's yield equ... |
| abbid 2804 | Equivalent wff's yield equ... |
| abbi 2805 | Equivalent formulas define... |
| cbvabv 2806 | Rule used to change bound ... |
| cbvabw 2807 | Rule used to change bound ... |
| cbvabwOLD 2808 | Obsolete version of ~ cbva... |
| cbvab 2809 | Rule used to change bound ... |
| abeq2w 2810 | Version of ~ abeq2 using i... |
| dfclel 2812 | Characterization of the el... |
| elissetv 2813 | An element of a class exis... |
| elisset 2814 | An element of a class exis... |
| eleq1w 2815 | Weaker version of ~ eleq1 ... |
| eleq2w 2816 | Weaker version of ~ eleq2 ... |
| eleq1d 2817 | Deduction from equality to... |
| eleq2d 2818 | Deduction from equality to... |
| eleq2dALT 2819 | Alternate proof of ~ eleq2... |
| eleq1 2820 | Equality implies equivalen... |
| eleq2 2821 | Equality implies equivalen... |
| eleq12 2822 | Equality implies equivalen... |
| eleq1i 2823 | Inference from equality to... |
| eleq2i 2824 | Inference from equality to... |
| eleq12i 2825 | Inference from equality to... |
| eqneltri 2826 | If a class is not an eleme... |
| eleq12d 2827 | Deduction from equality to... |
| eleq1a 2828 | A transitive-type law rela... |
| eqeltri 2829 | Substitution of equal clas... |
| eqeltrri 2830 | Substitution of equal clas... |
| eleqtri 2831 | Substitution of equal clas... |
| eleqtrri 2832 | Substitution of equal clas... |
| eqeltrd 2833 | Substitution of equal clas... |
| eqeltrrd 2834 | Deduction that substitutes... |
| eleqtrd 2835 | Deduction that substitutes... |
| eleqtrrd 2836 | Deduction that substitutes... |
| eqeltrid 2837 | A membership and equality ... |
| eqeltrrid 2838 | A membership and equality ... |
| eleqtrid 2839 | A membership and equality ... |
| eleqtrrid 2840 | A membership and equality ... |
| eqeltrdi 2841 | A membership and equality ... |
| eqeltrrdi 2842 | A membership and equality ... |
| eleqtrdi 2843 | A membership and equality ... |
| eleqtrrdi 2844 | A membership and equality ... |
| 3eltr3i 2845 | Substitution of equal clas... |
| 3eltr4i 2846 | Substitution of equal clas... |
| 3eltr3d 2847 | Substitution of equal clas... |
| 3eltr4d 2848 | Substitution of equal clas... |
| 3eltr3g 2849 | Substitution of equal clas... |
| 3eltr4g 2850 | Substitution of equal clas... |
| eleq2s 2851 | Substitution of equal clas... |
| eqneltrd 2852 | If a class is not an eleme... |
| eqneltrrd 2853 | If a class is not an eleme... |
| neleqtrd 2854 | If a class is not an eleme... |
| neleqtrrd 2855 | If a class is not an eleme... |
| cleqh 2856 | Establish equality between... |
| nelneq 2857 | A way of showing two class... |
| nelneq2 2858 | A way of showing two class... |
| eqsb3 2859 | Substitution applied to an... |
| clelsb3 2860 | Substitution applied to an... |
| hbxfreq 2861 | A utility lemma to transfe... |
| hblem 2862 | Change the free variable o... |
| hblemg 2863 | Change the free variable o... |
| abeq2 2864 | Equality of a class variab... |
| abeq1 2865 | Equality of a class variab... |
| abeq2d 2866 | Equality of a class variab... |
| abeq2i 2867 | Equality of a class variab... |
| abeq1i 2868 | Equality of a class variab... |
| abbi2dv 2869 | Deduction from a wff to a ... |
| abbi1dv 2870 | Deduction from a wff to a ... |
| abbi2i 2871 | Equality of a class variab... |
| abbiOLD 2872 | Obsolete proof of ~ abbi a... |
| abid1 2873 | Every class is equal to a ... |
| abid2 2874 | A simplification of class ... |
| clelab 2875 | Membership of a class vari... |
| clelabOLD 2876 | Obsolete version of ~ clel... |
| clabel 2877 | Membership of a class abst... |
| sbab 2878 | The right-hand side of the... |
| nfcjust 2880 | Justification theorem for ... |
| nfci 2882 | Deduce that a class ` A ` ... |
| nfcii 2883 | Deduce that a class ` A ` ... |
| nfcr 2884 | Consequence of the not-fre... |
| nfcrALT 2885 | Alternate version of ~ nfc... |
| nfcri 2886 | Consequence of the not-fre... |
| nfcd 2887 | Deduce that a class ` A ` ... |
| nfcrd 2888 | Consequence of the not-fre... |
| nfcriOLD 2889 | Obsolete version of ~ nfcr... |
| nfcriOLDOLD 2890 | Obsolete version of ~ nfcr... |
| nfcrii 2891 | Consequence of the not-fre... |
| nfcriiOLD 2892 | Obsolete version of ~ nfcr... |
| nfcriOLDOLDOLD 2893 | Obsolete version of ~ nfcr... |
| nfceqdf 2894 | An equality theorem for ef... |
| nfceqdfOLD 2895 | Obsolete version of ~ nfce... |
| nfceqi 2896 | Equality theorem for class... |
| nfcxfr 2897 | A utility lemma to transfe... |
| nfcxfrd 2898 | A utility lemma to transfe... |
| nfcv 2899 | If ` x ` is disjoint from ... |
| nfcvd 2900 | If ` x ` is disjoint from ... |
| nfab1 2901 | Bound-variable hypothesis ... |
| nfnfc1 2902 | The setvar ` x ` is bound ... |
| clelsb3fw 2903 | Substitution applied to an... |
| clelsb3f 2904 | Substitution applied to an... |
| nfab 2905 | Bound-variable hypothesis ... |
| nfabg 2906 | Bound-variable hypothesis ... |
| nfaba1 2907 | Bound-variable hypothesis ... |
| nfaba1g 2908 | Bound-variable hypothesis ... |
| nfeqd 2909 | Hypothesis builder for equ... |
| nfeld 2910 | Hypothesis builder for ele... |
| nfnfc 2911 | Hypothesis builder for ` F... |
| nfeq 2912 | Hypothesis builder for equ... |
| nfel 2913 | Hypothesis builder for ele... |
| nfeq1 2914 | Hypothesis builder for equ... |
| nfel1 2915 | Hypothesis builder for ele... |
| nfeq2 2916 | Hypothesis builder for equ... |
| nfel2 2917 | Hypothesis builder for ele... |
| drnfc1 2918 | Formula-building lemma for... |
| drnfc1OLD 2919 | Obsolete version of ~ drnf... |
| drnfc2 2920 | Formula-building lemma for... |
| drnfc2OLD 2921 | Obsolete version of ~ drnf... |
| nfabdw 2922 | Bound-variable hypothesis ... |
| nfabdwOLD 2923 | Obsolete version of ~ nfab... |
| nfabd 2924 | Bound-variable hypothesis ... |
| nfabd2 2925 | Bound-variable hypothesis ... |
| dvelimdc 2926 | Deduction form of ~ dvelim... |
| dvelimc 2927 | Version of ~ dvelim for cl... |
| nfcvf 2928 | If ` x ` and ` y ` are dis... |
| nfcvf2 2929 | If ` x ` and ` y ` are dis... |
| cleqf 2930 | Establish equality between... |
| abid2f 2931 | A simplification of class ... |
| abeq2f 2932 | Equality of a class variab... |
| sbabel 2933 | Theorem to move a substitu... |
| neii 2936 | Inference associated with ... |
| neir 2937 | Inference associated with ... |
| nne 2938 | Negation of inequality. (... |
| neneqd 2939 | Deduction eliminating ineq... |
| neneq 2940 | From inequality to non-equ... |
| neqned 2941 | If it is not the case that... |
| neqne 2942 | From non-equality to inequ... |
| neirr 2943 | No class is unequal to its... |
| exmidne 2944 | Excluded middle with equal... |
| eqneqall 2945 | A contradiction concerning... |
| nonconne 2946 | Law of noncontradiction wi... |
| necon3ad 2947 | Contrapositive law deducti... |
| necon3bd 2948 | Contrapositive law deducti... |
| necon2ad 2949 | Contrapositive inference f... |
| necon2bd 2950 | Contrapositive inference f... |
| necon1ad 2951 | Contrapositive deduction f... |
| necon1bd 2952 | Contrapositive deduction f... |
| necon4ad 2953 | Contrapositive inference f... |
| necon4bd 2954 | Contrapositive inference f... |
| necon3d 2955 | Contrapositive law deducti... |
| necon1d 2956 | Contrapositive law deducti... |
| necon2d 2957 | Contrapositive inference f... |
| necon4d 2958 | Contrapositive inference f... |
| necon3ai 2959 | Contrapositive inference f... |
| necon3bi 2960 | Contrapositive inference f... |
| necon1ai 2961 | Contrapositive inference f... |
| necon1bi 2962 | Contrapositive inference f... |
| necon2ai 2963 | Contrapositive inference f... |
| necon2bi 2964 | Contrapositive inference f... |
| necon4ai 2965 | Contrapositive inference f... |
| necon3i 2966 | Contrapositive inference f... |
| necon1i 2967 | Contrapositive inference f... |
| necon2i 2968 | Contrapositive inference f... |
| necon4i 2969 | Contrapositive inference f... |
| necon3abid 2970 | Deduction from equality to... |
| necon3bbid 2971 | Deduction from equality to... |
| necon1abid 2972 | Contrapositive deduction f... |
| necon1bbid 2973 | Contrapositive inference f... |
| necon4abid 2974 | Contrapositive law deducti... |
| necon4bbid 2975 | Contrapositive law deducti... |
| necon2abid 2976 | Contrapositive deduction f... |
| necon2bbid 2977 | Contrapositive deduction f... |
| necon3bid 2978 | Deduction from equality to... |
| necon4bid 2979 | Contrapositive law deducti... |
| necon3abii 2980 | Deduction from equality to... |
| necon3bbii 2981 | Deduction from equality to... |
| necon1abii 2982 | Contrapositive inference f... |
| necon1bbii 2983 | Contrapositive inference f... |
| necon2abii 2984 | Contrapositive inference f... |
| necon2bbii 2985 | Contrapositive inference f... |
| necon3bii 2986 | Inference from equality to... |
| necom 2987 | Commutation of inequality.... |
| necomi 2988 | Inference from commutative... |
| necomd 2989 | Deduction from commutative... |
| nesym 2990 | Characterization of inequa... |
| nesymi 2991 | Inference associated with ... |
| nesymir 2992 | Inference associated with ... |
| neeq1d 2993 | Deduction for inequality. ... |
| neeq2d 2994 | Deduction for inequality. ... |
| neeq12d 2995 | Deduction for inequality. ... |
| neeq1 2996 | Equality theorem for inequ... |
| neeq2 2997 | Equality theorem for inequ... |
| neeq1i 2998 | Inference for inequality. ... |
| neeq2i 2999 | Inference for inequality. ... |
| neeq12i 3000 | Inference for inequality. ... |
| eqnetrd 3001 | Substitution of equal clas... |
| eqnetrrd 3002 | Substitution of equal clas... |
| neeqtrd 3003 | Substitution of equal clas... |
| eqnetri 3004 | Substitution of equal clas... |
| eqnetrri 3005 | Substitution of equal clas... |
| neeqtri 3006 | Substitution of equal clas... |
| neeqtrri 3007 | Substitution of equal clas... |
| neeqtrrd 3008 | Substitution of equal clas... |
| eqnetrrid 3009 | A chained equality inferen... |
| 3netr3d 3010 | Substitution of equality i... |
| 3netr4d 3011 | Substitution of equality i... |
| 3netr3g 3012 | Substitution of equality i... |
| 3netr4g 3013 | Substitution of equality i... |
| nebi 3014 | Contraposition law for ine... |
| pm13.18 3015 | Theorem *13.18 in [Whitehe... |
| pm13.181 3016 | Theorem *13.181 in [Whiteh... |
| pm2.61ine 3017 | Inference eliminating an i... |
| pm2.21ddne 3018 | A contradiction implies an... |
| pm2.61ne 3019 | Deduction eliminating an i... |
| pm2.61dne 3020 | Deduction eliminating an i... |
| pm2.61dane 3021 | Deduction eliminating an i... |
| pm2.61da2ne 3022 | Deduction eliminating two ... |
| pm2.61da3ne 3023 | Deduction eliminating thre... |
| pm2.61iine 3024 | Equality version of ~ pm2.... |
| neor 3025 | Logical OR with an equalit... |
| neanior 3026 | A De Morgan's law for ineq... |
| ne3anior 3027 | A De Morgan's law for ineq... |
| neorian 3028 | A De Morgan's law for ineq... |
| nemtbir 3029 | An inference from an inequ... |
| nelne1 3030 | Two classes are different ... |
| nelne2 3031 | Two classes are different ... |
| nelelne 3032 | Two classes are different ... |
| neneor 3033 | If two classes are differe... |
| nfne 3034 | Bound-variable hypothesis ... |
| nfned 3035 | Bound-variable hypothesis ... |
| nabbi 3036 | Not equivalent wff's corre... |
| mteqand 3037 | A modus tollens deduction ... |
| neli 3040 | Inference associated with ... |
| nelir 3041 | Inference associated with ... |
| neleq12d 3042 | Equality theorem for negat... |
| neleq1 3043 | Equality theorem for negat... |
| neleq2 3044 | Equality theorem for negat... |
| nfnel 3045 | Bound-variable hypothesis ... |
| nfneld 3046 | Bound-variable hypothesis ... |
| nnel 3047 | Negation of negated member... |
| elnelne1 3048 | Two classes are different ... |
| elnelne2 3049 | Two classes are different ... |
| nelcon3d 3050 | Contrapositive law deducti... |
| elnelall 3051 | A contradiction concerning... |
| pm2.61danel 3052 | Deduction eliminating an e... |
| rgen 3063 | Generalization rule for re... |
| ralel 3064 | All elements of a class ar... |
| rgenw 3065 | Generalization rule for re... |
| rgen2w 3066 | Generalization rule for re... |
| mprg 3067 | Modus ponens combined with... |
| mprgbir 3068 | Modus ponens on biconditio... |
| alral 3069 | Universal quantification i... |
| raln 3070 | Restricted universally qua... |
| ral2imi 3071 | Inference quantifying ante... |
| ralimi2 3072 | Inference quantifying both... |
| ralimia 3073 | Inference quantifying both... |
| ralimiaa 3074 | Inference quantifying both... |
| ralimi 3075 | Inference quantifying both... |
| 2ralimi 3076 | Inference quantifying both... |
| ralim 3077 | Distribution of restricted... |
| ralbii2 3078 | Inference adding different... |
| ralbiia 3079 | Inference adding restricte... |
| ralbii 3080 | Inference adding restricte... |
| 2ralbii 3081 | Inference adding two restr... |
| ralbi 3082 | Distribute a restricted un... |
| ralanid 3083 | Cancellation law for restr... |
| r19.26 3084 | Restricted quantifier vers... |
| r19.26-2 3085 | Restricted quantifier vers... |
| r19.26-3 3086 | Version of ~ r19.26 with t... |
| r19.26m 3087 | Version of ~ 19.26 and ~ r... |
| ralbiim 3088 | Split a biconditional and ... |
| r19.21v 3089 | Restricted quantifier vers... |
| ralimdv2 3090 | Inference quantifying both... |
| ralimdva 3091 | Deduction quantifying both... |
| ralimdv 3092 | Deduction quantifying both... |
| ralimdvva 3093 | Deduction doubly quantifyi... |
| hbralrimi 3094 | Inference from Theorem 19.... |
| ralrimiv 3095 | Inference from Theorem 19.... |
| ralrimiva 3096 | Inference from Theorem 19.... |
| ralrimivw 3097 | Inference from Theorem 19.... |
| r19.27v 3098 | Restricted quantitifer ver... |
| r19.28v 3099 | Restricted quantifier vers... |
| ralrimdv 3100 | Inference from Theorem 19.... |
| ralrimdva 3101 | Inference from Theorem 19.... |
| ralrimivv 3102 | Inference from Theorem 19.... |
| ralrimivva 3103 | Inference from Theorem 19.... |
| ralrimivvva 3104 | Inference from Theorem 19.... |
| ralrimdvv 3105 | Inference from Theorem 19.... |
| ralrimdvva 3106 | Inference from Theorem 19.... |
| ralbidv2 3107 | Formula-building rule for ... |
| ralbidva 3108 | Formula-building rule for ... |
| ralbidv 3109 | Formula-building rule for ... |
| 2ralbidva 3110 | Formula-building rule for ... |
| 2ralbidv 3111 | Formula-building rule for ... |
| r2allem 3112 | Lemma factoring out common... |
| r2al 3113 | Double restricted universa... |
| r3al 3114 | Triple restricted universa... |
| rgen2 3115 | Generalization rule for re... |
| rgen3 3116 | Generalization rule for re... |
| rsp 3117 | Restricted specialization.... |
| rspa 3118 | Restricted specialization.... |
| rspec 3119 | Specialization rule for re... |
| r19.21bi 3120 | Inference from Theorem 19.... |
| r19.21be 3121 | Inference from Theorem 19.... |
| rspec2 3122 | Specialization rule for re... |
| rspec3 3123 | Specialization rule for re... |
| rsp2 3124 | Restricted specialization,... |
| r19.21t 3125 | Restricted quantifier vers... |
| r19.21 3126 | Restricted quantifier vers... |
| ralrimi 3127 | Inference from Theorem 19.... |
| ralimdaa 3128 | Deduction quantifying both... |
| ralrimd 3129 | Inference from Theorem 19.... |
| nfra1 3130 | The setvar ` x ` is not fr... |
| hbra1 3131 | The setvar ` x ` is not fr... |
| hbral 3132 | Bound-variable hypothesis ... |
| r2alf 3133 | Double restricted universa... |
| nfraldw 3134 | Deduction version of ~ nfr... |
| nfraldwOLD 3135 | Obsolete version of ~ nfra... |
| nfrald 3136 | Deduction version of ~ nfr... |
| nfralw 3137 | Bound-variable hypothesis ... |
| nfral 3138 | Bound-variable hypothesis ... |
| nfra2w 3139 | Similar to Lemma 24 of [Mo... |
| nfra2wOLD 3140 | Obsolete version of ~ nfra... |
| nfra2 3141 | Similar to Lemma 24 of [Mo... |
| rgen2a 3142 | Generalization rule for re... |
| ralbida 3143 | Formula-building rule for ... |
| ralbid 3144 | Formula-building rule for ... |
| 2ralbida 3145 | Formula-building rule for ... |
| raleqbii 3146 | Equality deduction for res... |
| ralcom4 3147 | Commutation of restricted ... |
| ralnex 3148 | Relationship between restr... |
| dfral2 3149 | Relationship between restr... |
| rexnal 3150 | Relationship between restr... |
| dfrex2 3151 | Relationship between restr... |
| rexex 3152 | Restricted existence impli... |
| rexim 3153 | Theorem 19.22 of [Margaris... |
| rexbi 3154 | Distribute restricted quan... |
| reximia 3155 | Inference quantifying both... |
| reximi 3156 | Inference quantifying both... |
| reximi2 3157 | Inference quantifying both... |
| rexbii2 3158 | Inference adding different... |
| rexbiia 3159 | Inference adding restricte... |
| rexbii 3160 | Inference adding restricte... |
| 2rexbii 3161 | Inference adding two restr... |
| rexcom4 3162 | Commutation of restricted ... |
| 2ex2rexrot 3163 | Rotate two existential qua... |
| rexcom4a 3164 | Specialized existential co... |
| rexanid 3165 | Cancellation law for restr... |
| r19.29 3166 | Restricted quantifier vers... |
| r19.29r 3167 | Restricted quantifier vers... |
| r19.29imd 3168 | Theorem 19.29 of [Margaris... |
| rexnal2 3169 | Relationship between two r... |
| rexnal3 3170 | Relationship between three... |
| ralnex2 3171 | Relationship between two r... |
| ralnex3 3172 | Relationship between three... |
| ralinexa 3173 | A transformation of restri... |
| rexanali 3174 | A transformation of restri... |
| nrexralim 3175 | Negation of a complex pred... |
| risset 3176 | Two ways to say " ` A ` be... |
| nelb 3177 | A definition of ` -. A e. ... |
| nrex 3178 | Inference adding restricte... |
| nrexdv 3179 | Deduction adding restricte... |
| reximdv2 3180 | Deduction quantifying both... |
| reximdvai 3181 | Deduction quantifying both... |
| reximdv 3182 | Deduction from Theorem 19.... |
| reximdva 3183 | Deduction quantifying both... |
| reximddv 3184 | Deduction from Theorem 19.... |
| reximssdv 3185 | Derivation of a restricted... |
| reximdvva 3186 | Deduction doubly quantifyi... |
| reximddv2 3187 | Double deduction from Theo... |
| r19.23v 3188 | Restricted quantifier vers... |
| rexlimiv 3189 | Inference from Theorem 19.... |
| rexlimiva 3190 | Inference from Theorem 19.... |
| rexlimivw 3191 | Weaker version of ~ rexlim... |
| rexlimdv 3192 | Inference from Theorem 19.... |
| rexlimdva 3193 | Inference from Theorem 19.... |
| rexlimdvaa 3194 | Inference from Theorem 19.... |
| rexlimdv3a 3195 | Inference from Theorem 19.... |
| rexlimdva2 3196 | Inference from Theorem 19.... |
| r19.29an 3197 | A commonly used pattern in... |
| r19.29a 3198 | A commonly used pattern in... |
| rexlimdvw 3199 | Inference from Theorem 19.... |
| rexlimddv 3200 | Restricted existential eli... |
| rexlimivv 3201 | Inference from Theorem 19.... |
| rexlimdvv 3202 | Inference from Theorem 19.... |
| rexlimdvva 3203 | Inference from Theorem 19.... |
| rexbidv2 3204 | Formula-building rule for ... |
| rexbidva 3205 | Formula-building rule for ... |
| rexbidv 3206 | Formula-building rule for ... |
| 2rexbiia 3207 | Inference adding two restr... |
| 2rexbidva 3208 | Formula-building rule for ... |
| 2rexbidv 3209 | Formula-building rule for ... |
| rexralbidv 3210 | Formula-building rule for ... |
| r2exlem 3211 | Lemma factoring out common... |
| r2ex 3212 | Double restricted existent... |
| rspe 3213 | Restricted specialization.... |
| rsp2e 3214 | Restricted specialization.... |
| nfre1 3215 | The setvar ` x ` is not fr... |
| nfrexd 3216 | Deduction version of ~ nfr... |
| nfrexdg 3217 | Deduction version of ~ nfr... |
| nfrex 3218 | Bound-variable hypothesis ... |
| nfrexg 3219 | Bound-variable hypothesis ... |
| reximdai 3220 | Deduction from Theorem 19.... |
| reximd2a 3221 | Deduction quantifying both... |
| r19.23t 3222 | Closed theorem form of ~ r... |
| r19.23 3223 | Restricted quantifier vers... |
| rexlimi 3224 | Restricted quantifier vers... |
| rexlimd2 3225 | Version of ~ rexlimd with ... |
| rexlimd 3226 | Deduction form of ~ rexlim... |
| rexbida 3227 | Formula-building rule for ... |
| rexbidvaALT 3228 | Alternate proof of ~ rexbi... |
| rexbid 3229 | Formula-building rule for ... |
| rexbidvALT 3230 | Alternate proof of ~ rexbi... |
| ralrexbid 3231 | Formula-building rule for ... |
| ralrexbidOLD 3232 | Obsolete version of ~ ralr... |
| r19.12 3233 | Restricted quantifier vers... |
| r2exf 3234 | Double restricted existent... |
| rexeqbii 3235 | Equality deduction for res... |
| reuanid 3236 | Cancellation law for restr... |
| rmoanid 3237 | Cancellation law for restr... |
| r19.29af2 3238 | A commonly used pattern ba... |
| r19.29af 3239 | A commonly used pattern ba... |
| 2r19.29 3240 | Theorem ~ r19.29 with two ... |
| r19.29d2r 3241 | Theorem 19.29 of [Margaris... |
| r19.29vva 3242 | A commonly used pattern ba... |
| r19.30 3243 | Restricted quantifier vers... |
| r19.32v 3244 | Restricted quantifier vers... |
| r19.35 3245 | Restricted quantifier vers... |
| r19.36v 3246 | Restricted quantifier vers... |
| r19.37 3247 | Restricted quantifier vers... |
| r19.37v 3248 | Restricted quantifier vers... |
| r19.40 3249 | Restricted quantifier vers... |
| r19.41v 3250 | Restricted quantifier vers... |
| r19.41 3251 | Restricted quantifier vers... |
| r19.41vv 3252 | Version of ~ r19.41v with ... |
| r19.42v 3253 | Restricted quantifier vers... |
| r19.43 3254 | Restricted quantifier vers... |
| r19.44v 3255 | One direction of a restric... |
| r19.45v 3256 | Restricted quantifier vers... |
| ralcom 3257 | Commutation of restricted ... |
| rexcom 3258 | Commutation of restricted ... |
| ralcomf 3259 | Commutation of restricted ... |
| rexcomf 3260 | Commutation of restricted ... |
| ralcom13 3261 | Swap first and third restr... |
| rexcom13 3262 | Swap first and third restr... |
| ralrot3 3263 | Rotate three restricted un... |
| rexrot4 3264 | Rotate four restricted exi... |
| ralcom2 3265 | Commutation of restricted ... |
| ralcom3 3266 | A commutation law for rest... |
| reeanlem 3267 | Lemma factoring out common... |
| reean 3268 | Rearrange restricted exist... |
| reeanv 3269 | Rearrange restricted exist... |
| 3reeanv 3270 | Rearrange three restricted... |
| 2ralor 3271 | Distribute restricted univ... |
| nfreu1 3272 | The setvar ` x ` is not fr... |
| nfrmo1 3273 | The setvar ` x ` is not fr... |
| nfreud 3274 | Deduction version of ~ nfr... |
| nfrmod 3275 | Deduction version of ~ nfr... |
| nfreuw 3276 | Bound-variable hypothesis ... |
| nfrmow 3277 | Bound-variable hypothesis ... |
| nfreu 3278 | Bound-variable hypothesis ... |
| nfrmo 3279 | Bound-variable hypothesis ... |
| rabid 3280 | An "identity" law of concr... |
| rabrab 3281 | Abstract builder restricte... |
| rabidim1 3282 | Membership in a restricted... |
| rabid2 3283 | An "identity" law for rest... |
| rabid2f 3284 | An "identity" law for rest... |
| rabbi 3285 | Equivalent wff's correspon... |
| nfrab1 3286 | The abstraction variable i... |
| nfrabw 3287 | A variable not free in a w... |
| nfrab 3288 | A variable not free in a w... |
| reubida 3289 | Formula-building rule for ... |
| reubidva 3290 | Formula-building rule for ... |
| reubidv 3291 | Formula-building rule for ... |
| reubiia 3292 | Formula-building rule for ... |
| reubii 3293 | Formula-building rule for ... |
| rmobida 3294 | Formula-building rule for ... |
| rmobidva 3295 | Formula-building rule for ... |
| rmobidv 3296 | Formula-building rule for ... |
| rmobiia 3297 | Formula-building rule for ... |
| rmobii 3298 | Formula-building rule for ... |
| raleqf 3299 | Equality theorem for restr... |
| rexeqf 3300 | Equality theorem for restr... |
| reueq1f 3301 | Equality theorem for restr... |
| rmoeq1f 3302 | Equality theorem for restr... |
| raleqbidv 3303 | Equality deduction for res... |
| rexeqbidv 3304 | Equality deduction for res... |
| raleqbidvv 3305 | Version of ~ raleqbidv wit... |
| rexeqbidvv 3306 | Version of ~ rexeqbidv wit... |
| raleqbi1dv 3307 | Equality deduction for res... |
| rexeqbi1dv 3308 | Equality deduction for res... |
| raleq 3309 | Equality theorem for restr... |
| rexeq 3310 | Equality theorem for restr... |
| reueq1 3311 | Equality theorem for restr... |
| rmoeq1 3312 | Equality theorem for restr... |
| raleqi 3313 | Equality inference for res... |
| rexeqi 3314 | Equality inference for res... |
| raleqdv 3315 | Equality deduction for res... |
| rexeqdv 3316 | Equality deduction for res... |
| reueqd 3317 | Equality deduction for res... |
| rmoeqd 3318 | Equality deduction for res... |
| raleqbid 3319 | Equality deduction for res... |
| rexeqbid 3320 | Equality deduction for res... |
| raleqbidva 3321 | Equality deduction for res... |
| rexeqbidva 3322 | Equality deduction for res... |
| raleleq 3323 | All elements of a class ar... |
| raleleqALT 3324 | Alternate proof of ~ ralel... |
| moel 3325 | "At most one" element in a... |
| mormo 3326 | Unrestricted "at most one"... |
| reu5 3327 | Restricted uniqueness in t... |
| reurex 3328 | Restricted unique existenc... |
| 2reu2rex 3329 | Double restricted existent... |
| reurmo 3330 | Restricted existential uni... |
| rmo5 3331 | Restricted "at most one" i... |
| nrexrmo 3332 | Nonexistence implies restr... |
| reueubd 3333 | Restricted existential uni... |
| cbvralfw 3334 | Rule used to change bound ... |
| cbvralfwOLD 3335 | Obsolete version of ~ cbvr... |
| cbvrexfw 3336 | Rule used to change bound ... |
| cbvralf 3337 | Rule used to change bound ... |
| cbvrexf 3338 | Rule used to change bound ... |
| cbvralw 3339 | Rule used to change bound ... |
| cbvrexw 3340 | Rule used to change bound ... |
| cbvreuw 3341 | Change the bound variable ... |
| cbvrmow 3342 | Change the bound variable ... |
| cbvrmowOLD 3343 | Obsolete version of ~ cbvr... |
| cbvral 3344 | Rule used to change bound ... |
| cbvrex 3345 | Rule used to change bound ... |
| cbvreu 3346 | Change the bound variable ... |
| cbvrmo 3347 | Change the bound variable ... |
| cbvralvw 3348 | Change the bound variable ... |
| cbvrexvw 3349 | Change the bound variable ... |
| cbvrmovw 3350 | Change the bound variable ... |
| cbvreuvw 3351 | Change the bound variable ... |
| cbvreuvwOLD 3352 | Obsolete version of ~ cbvr... |
| cbvralv 3353 | Change the bound variable ... |
| cbvrexv 3354 | Change the bound variable ... |
| cbvreuv 3355 | Change the bound variable ... |
| cbvrmov 3356 | Change the bound variable ... |
| cbvraldva2 3357 | Rule used to change the bo... |
| cbvrexdva2 3358 | Rule used to change the bo... |
| cbvraldva 3359 | Rule used to change the bo... |
| cbvrexdva 3360 | Rule used to change the bo... |
| cbvral2vw 3361 | Change bound variables of ... |
| cbvrex2vw 3362 | Change bound variables of ... |
| cbvral3vw 3363 | Change bound variables of ... |
| cbvral2v 3364 | Change bound variables of ... |
| cbvrex2v 3365 | Change bound variables of ... |
| cbvral3v 3366 | Change bound variables of ... |
| cbvralsvw 3367 | Change bound variable by u... |
| cbvrexsvw 3368 | Change bound variable by u... |
| cbvralsv 3369 | Change bound variable by u... |
| cbvrexsv 3370 | Change bound variable by u... |
| sbralie 3371 | Implicit to explicit subst... |
| rabbiia 3372 | Equivalent formulas yield ... |
| rabbii 3373 | Equivalent wff's correspon... |
| rabbida 3374 | Equivalent wff's yield equ... |
| rabbid 3375 | Version of ~ rabbidv with ... |
| rabbidva2 3376 | Equivalent wff's yield equ... |
| rabbia2 3377 | Equivalent wff's yield equ... |
| rabbidva 3378 | Equivalent wff's yield equ... |
| rabbidvaOLD 3379 | Obsolete proof of ~ rabbid... |
| rabbidv 3380 | Equivalent wff's yield equ... |
| rabeqf 3381 | Equality theorem for restr... |
| rabeqi 3382 | Equality theorem for restr... |
| rabeqiOLD 3383 | Obsolete version of ~ rabe... |
| rabeq 3384 | Equality theorem for restr... |
| rabeqdv 3385 | Equality of restricted cla... |
| rabeqbidv 3386 | Equality of restricted cla... |
| rabeqbidva 3387 | Equality of restricted cla... |
| rabeq2i 3388 | Inference from equality of... |
| rabswap 3389 | Swap with a membership rel... |
| cbvrabw 3390 | Rule to change the bound v... |
| cbvrab 3391 | Rule to change the bound v... |
| cbvrabv 3392 | Rule to change the bound v... |
| rabrabi 3393 | Abstract builder restricte... |
| rabeqcda 3394 | When ` ps ` is always true... |
| ralrimia 3395 | Inference from Theorem 19.... |
| ralimda 3396 | Deduction quantifying both... |
| vjust 3398 | Justification theorem for ... |
| dfv2 3400 | Alternate definition of th... |
| vex 3401 | All setvar variables are s... |
| vexOLD 3402 | Obsolete version of ~ vex ... |
| elv 3403 | If a proposition is implie... |
| elvd 3404 | If a proposition is implie... |
| el2v 3405 | If a proposition is implie... |
| eqv 3406 | The universe contains ever... |
| eqvf 3407 | The universe contains ever... |
| abv 3408 | The class of sets verifyin... |
| abvALT 3409 | Alternate proof of ~ abv ,... |
| isset 3410 | Two ways to express that "... |
| issetf 3411 | A version of ~ isset that ... |
| isseti 3412 | A way to say " ` A ` is a ... |
| issetri 3413 | A way to say " ` A ` is a ... |
| eqvisset 3414 | A class equal to a variabl... |
| elex 3415 | If a class is a member of ... |
| elexi 3416 | If a class is a member of ... |
| elexd 3417 | If a class is a member of ... |
| elex2 3418 | If a class contains anothe... |
| elex22 3419 | If two classes each contai... |
| prcnel 3420 | A proper class doesn't bel... |
| ralv 3421 | A universal quantifier res... |
| rexv 3422 | An existential quantifier ... |
| reuv 3423 | A unique existential quant... |
| rmov 3424 | An at-most-one quantifier ... |
| rabab 3425 | A class abstraction restri... |
| rexcom4b 3426 | Specialized existential co... |
| ceqsalt 3427 | Closed theorem version of ... |
| ceqsralt 3428 | Restricted quantifier vers... |
| ceqsalg 3429 | A representation of explic... |
| ceqsalgALT 3430 | Alternate proof of ~ ceqsa... |
| ceqsal 3431 | A representation of explic... |
| ceqsalv 3432 | A representation of explic... |
| ceqsalvOLD 3433 | Obsolete version of ~ ceqs... |
| ceqsralv 3434 | Restricted quantifier vers... |
| ceqsralvOLD 3435 | Obsolete version of ~ ceqs... |
| gencl 3436 | Implicit substitution for ... |
| 2gencl 3437 | Implicit substitution for ... |
| 3gencl 3438 | Implicit substitution for ... |
| cgsexg 3439 | Implicit substitution infe... |
| cgsex2g 3440 | Implicit substitution infe... |
| cgsex4g 3441 | An implicit substitution i... |
| cgsex4gOLD 3442 | Obsolete version of ~ cgse... |
| ceqsex 3443 | Elimination of an existent... |
| ceqsexv 3444 | Elimination of an existent... |
| ceqsexv2d 3445 | Elimination of an existent... |
| ceqsex2 3446 | Elimination of two existen... |
| ceqsex2v 3447 | Elimination of two existen... |
| ceqsex3v 3448 | Elimination of three exist... |
| ceqsex4v 3449 | Elimination of four existe... |
| ceqsex6v 3450 | Elimination of six existen... |
| ceqsex8v 3451 | Elimination of eight exist... |
| gencbvex 3452 | Change of bound variable u... |
| gencbvex2 3453 | Restatement of ~ gencbvex ... |
| gencbval 3454 | Change of bound variable u... |
| sbhypf 3455 | Introduce an explicit subs... |
| vtoclgft 3456 | Closed theorem form of ~ v... |
| vtoclgftOLD 3457 | Obsolete version of ~ vtoc... |
| vtocldf 3458 | Implicit substitution of a... |
| vtocld 3459 | Implicit substitution of a... |
| vtocldOLD 3460 | Obsolete version of ~ vtoc... |
| vtocl2d 3461 | Implicit substitution of t... |
| vtoclf 3462 | Implicit substitution of a... |
| vtocl 3463 | Implicit substitution of a... |
| vtoclALT 3464 | Alternate proof of ~ vtocl... |
| vtocl2 3465 | Implicit substitution of c... |
| vtocl3 3466 | Implicit substitution of c... |
| vtoclb 3467 | Implicit substitution of a... |
| vtoclgf 3468 | Implicit substitution of a... |
| vtoclg1f 3469 | Version of ~ vtoclgf with ... |
| vtoclg 3470 | Implicit substitution of a... |
| vtoclgOLD 3471 | Obsolete version of ~ vtoc... |
| vtoclbg 3472 | Implicit substitution of a... |
| vtocl2gf 3473 | Implicit substitution of a... |
| vtocl3gf 3474 | Implicit substitution of a... |
| vtocl2g 3475 | Implicit substitution of 2... |
| vtoclgaf 3476 | Implicit substitution of a... |
| vtoclga 3477 | Implicit substitution of a... |
| vtocl2ga 3478 | Implicit substitution of 2... |
| vtocl2gaf 3479 | Implicit substitution of 2... |
| vtocl3gaf 3480 | Implicit substitution of 3... |
| vtocl3ga 3481 | Implicit substitution of 3... |
| vtocl4g 3482 | Implicit substitution of 4... |
| vtocl4ga 3483 | Implicit substitution of 4... |
| vtocleg 3484 | Implicit substitution of a... |
| vtoclegft 3485 | Implicit substitution of a... |
| vtoclef 3486 | Implicit substitution of a... |
| vtocle 3487 | Implicit substitution of a... |
| vtoclri 3488 | Implicit substitution of a... |
| spcimgft 3489 | A closed version of ~ spci... |
| spcgft 3490 | A closed version of ~ spcg... |
| spcimgf 3491 | Rule of specialization, us... |
| spcimegf 3492 | Existential specialization... |
| spcgf 3493 | Rule of specialization, us... |
| spcegf 3494 | Existential specialization... |
| spcimdv 3495 | Restricted specialization,... |
| spcdv 3496 | Rule of specialization, us... |
| spcimedv 3497 | Restricted existential spe... |
| spcgv 3498 | Rule of specialization, us... |
| spcegv 3499 | Existential specialization... |
| spcedv 3500 | Existential specialization... |
| spc2egv 3501 | Existential specialization... |
| spc2gv 3502 | Specialization with two qu... |
| spc2ed 3503 | Existential specialization... |
| spc2d 3504 | Specialization with 2 quan... |
| spc3egv 3505 | Existential specialization... |
| spc3gv 3506 | Specialization with three ... |
| spcv 3507 | Rule of specialization, us... |
| spcev 3508 | Existential specialization... |
| spc2ev 3509 | Existential specialization... |
| rspct 3510 | A closed version of ~ rspc... |
| rspcdf 3511 | Restricted specialization,... |
| rspc 3512 | Restricted specialization,... |
| rspce 3513 | Restricted existential spe... |
| rspcimdv 3514 | Restricted specialization,... |
| rspcimedv 3515 | Restricted existential spe... |
| rspcdv 3516 | Restricted specialization,... |
| rspcedv 3517 | Restricted existential spe... |
| rspcebdv 3518 | Restricted existential spe... |
| rspcv 3519 | Restricted specialization,... |
| rspcvOLD 3520 | Obsolete version of ~ rspc... |
| rspccv 3521 | Restricted specialization,... |
| rspcva 3522 | Restricted specialization,... |
| rspccva 3523 | Restricted specialization,... |
| rspcev 3524 | Restricted existential spe... |
| rspcevOLD 3525 | Obsolete version of ~ rspc... |
| rspcdva 3526 | Restricted specialization,... |
| rspcedvd 3527 | Restricted existential spe... |
| rspcime 3528 | Prove a restricted existen... |
| rspceaimv 3529 | Restricted existential spe... |
| rspcedeq1vd 3530 | Restricted existential spe... |
| rspcedeq2vd 3531 | Restricted existential spe... |
| rspc2 3532 | Restricted specialization ... |
| rspc2gv 3533 | Restricted specialization ... |
| rspc2v 3534 | 2-variable restricted spec... |
| rspc2va 3535 | 2-variable restricted spec... |
| rspc2ev 3536 | 2-variable restricted exis... |
| rspc3v 3537 | 3-variable restricted spec... |
| rspc3ev 3538 | 3-variable restricted exis... |
| rspceeqv 3539 | Restricted existential spe... |
| ralxpxfr2d 3540 | Transfer a universal quant... |
| rexraleqim 3541 | Statement following from e... |
| eqvincg 3542 | A variable introduction la... |
| eqvinc 3543 | A variable introduction la... |
| eqvincf 3544 | A variable introduction la... |
| alexeqg 3545 | Two ways to express substi... |
| ceqex 3546 | Equality implies equivalen... |
| ceqsexg 3547 | A representation of explic... |
| ceqsexgv 3548 | Elimination of an existent... |
| ceqsexgvOLD 3549 | Obsolete version of ~ ceqs... |
| ceqsrexv 3550 | Elimination of a restricte... |
| ceqsrexbv 3551 | Elimination of a restricte... |
| ceqsrex2v 3552 | Elimination of a restricte... |
| clel2g 3553 | Alternate definition of me... |
| clel2gOLD 3554 | Obsolete version of ~ clel... |
| clel2 3555 | Alternate definition of me... |
| clel3g 3556 | Alternate definition of me... |
| clel3 3557 | Alternate definition of me... |
| clel4g 3558 | Alternate definition of me... |
| clel4 3559 | Alternate definition of me... |
| clel4OLD 3560 | Obsolete version of ~ clel... |
| clel5 3561 | Alternate definition of cl... |
| pm13.183 3562 | Compare theorem *13.183 in... |
| rr19.3v 3563 | Restricted quantifier vers... |
| rr19.28v 3564 | Restricted quantifier vers... |
| elabgt 3565 | Membership in a class abst... |
| elabgf 3566 | Membership in a class abst... |
| elabf 3567 | Membership in a class abst... |
| elabgw 3568 | Membership in a class abst... |
| elab2gw 3569 | Membership in a class abst... |
| elabg 3570 | Membership in a class abst... |
| elab 3571 | Membership in a class abst... |
| elab2g 3572 | Membership in a class abst... |
| elabd 3573 | Explicit demonstration the... |
| elab2 3574 | Membership in a class abst... |
| elab4g 3575 | Membership in a class abst... |
| elab3gf 3576 | Membership in a class abst... |
| elab3g 3577 | Membership in a class abst... |
| elab3 3578 | Membership in a class abst... |
| elrabi 3579 | Implication for the member... |
| elrabiOLD 3580 | Obsolete version of ~ elra... |
| elrabf 3581 | Membership in a restricted... |
| rabtru 3582 | Abstract builder using the... |
| rabeqc 3583 | A restricted class abstrac... |
| elrab3t 3584 | Membership in a restricted... |
| elrab 3585 | Membership in a restricted... |
| elrab3 3586 | Membership in a restricted... |
| elrabd 3587 | Membership in a restricted... |
| elrab2 3588 | Membership in a restricted... |
| elrab2w 3589 | Membership in a restricted... |
| ralab 3590 | Universal quantification o... |
| ralrab 3591 | Universal quantification o... |
| rexab 3592 | Existential quantification... |
| rexrab 3593 | Existential quantification... |
| ralab2 3594 | Universal quantification o... |
| ralab2OLD 3595 | Obsolete version of ~ rala... |
| ralrab2 3596 | Universal quantification o... |
| rexab2 3597 | Existential quantification... |
| rexab2OLD 3598 | Obsolete version of ~ rexa... |
| rexrab2 3599 | Existential quantification... |
| abidnf 3600 | Identity used to create cl... |
| dedhb 3601 | A deduction theorem for co... |
| nelrdva 3602 | Deduce negative membership... |
| eqeu 3603 | A condition which implies ... |
| moeq 3604 | There exists at most one s... |
| eueq 3605 | A class is a set if and on... |
| eueqi 3606 | There exists a unique set ... |
| eueq2 3607 | Equality has existential u... |
| eueq3 3608 | Equality has existential u... |
| moeq3 3609 | "At most one" property of ... |
| mosub 3610 | "At most one" remains true... |
| mo2icl 3611 | Theorem for inferring "at ... |
| mob2 3612 | Consequence of "at most on... |
| moi2 3613 | Consequence of "at most on... |
| mob 3614 | Equality implied by "at mo... |
| moi 3615 | Equality implied by "at mo... |
| morex 3616 | Derive membership from uni... |
| euxfr2w 3617 | Transfer existential uniqu... |
| euxfrw 3618 | Transfer existential uniqu... |
| euxfr2 3619 | Transfer existential uniqu... |
| euxfr 3620 | Transfer existential uniqu... |
| euind 3621 | Existential uniqueness via... |
| reu2 3622 | A way to express restricte... |
| reu6 3623 | A way to express restricte... |
| reu3 3624 | A way to express restricte... |
| reu6i 3625 | A condition which implies ... |
| eqreu 3626 | A condition which implies ... |
| rmo4 3627 | Restricted "at most one" u... |
| reu4 3628 | Restricted uniqueness usin... |
| reu7 3629 | Restricted uniqueness usin... |
| reu8 3630 | Restricted uniqueness usin... |
| rmo3f 3631 | Restricted "at most one" u... |
| rmo4f 3632 | Restricted "at most one" u... |
| reu2eqd 3633 | Deduce equality from restr... |
| reueq 3634 | Equality has existential u... |
| rmoeq 3635 | Equality's restricted exis... |
| rmoan 3636 | Restricted "at most one" s... |
| rmoim 3637 | Restricted "at most one" i... |
| rmoimia 3638 | Restricted "at most one" i... |
| rmoimi 3639 | Restricted "at most one" i... |
| rmoimi2 3640 | Restricted "at most one" i... |
| 2reu5a 3641 | Double restricted existent... |
| reuimrmo 3642 | Restricted uniqueness impl... |
| 2reuswap 3643 | A condition allowing swap ... |
| 2reuswap2 3644 | A condition allowing swap ... |
| reuxfrd 3645 | Transfer existential uniqu... |
| reuxfr 3646 | Transfer existential uniqu... |
| reuxfr1d 3647 | Transfer existential uniqu... |
| reuxfr1ds 3648 | Transfer existential uniqu... |
| reuxfr1 3649 | Transfer existential uniqu... |
| reuind 3650 | Existential uniqueness via... |
| 2rmorex 3651 | Double restricted quantifi... |
| 2reu5lem1 3652 | Lemma for ~ 2reu5 . Note ... |
| 2reu5lem2 3653 | Lemma for ~ 2reu5 . (Cont... |
| 2reu5lem3 3654 | Lemma for ~ 2reu5 . This ... |
| 2reu5 3655 | Double restricted existent... |
| 2reurex 3656 | Double restricted quantifi... |
| 2reurmo 3657 | Double restricted quantifi... |
| 2rmoswap 3658 | A condition allowing to sw... |
| 2rexreu 3659 | Double restricted existent... |
| cdeqi 3662 | Deduce conditional equalit... |
| cdeqri 3663 | Property of conditional eq... |
| cdeqth 3664 | Deduce conditional equalit... |
| cdeqnot 3665 | Distribute conditional equ... |
| cdeqal 3666 | Distribute conditional equ... |
| cdeqab 3667 | Distribute conditional equ... |
| cdeqal1 3668 | Distribute conditional equ... |
| cdeqab1 3669 | Distribute conditional equ... |
| cdeqim 3670 | Distribute conditional equ... |
| cdeqcv 3671 | Conditional equality for s... |
| cdeqeq 3672 | Distribute conditional equ... |
| cdeqel 3673 | Distribute conditional equ... |
| nfcdeq 3674 | If we have a conditional e... |
| nfccdeq 3675 | Variation of ~ nfcdeq for ... |
| rru 3676 | Relative version of Russel... |
| rruOLD 3677 | Obsolete version of ~ rru ... |
| ru 3678 | Russell's Paradox. Propos... |
| dfsbcq 3681 | Proper substitution of a c... |
| dfsbcq2 3682 | This theorem, which is sim... |
| sbsbc 3683 | Show that ~ df-sb and ~ df... |
| sbceq1d 3684 | Equality theorem for class... |
| sbceq1dd 3685 | Equality theorem for class... |
| sbceqbid 3686 | Equality theorem for class... |
| sbc8g 3687 | This is the closest we can... |
| sbc2or 3688 | The disjunction of two equ... |
| sbcex 3689 | By our definition of prope... |
| sbceq1a 3690 | Equality theorem for class... |
| sbceq2a 3691 | Equality theorem for class... |
| spsbc 3692 | Specialization: if a formu... |
| spsbcd 3693 | Specialization: if a formu... |
| sbcth 3694 | A substitution into a theo... |
| sbcthdv 3695 | Deduction version of ~ sbc... |
| sbcid 3696 | An identity theorem for su... |
| nfsbc1d 3697 | Deduction version of ~ nfs... |
| nfsbc1 3698 | Bound-variable hypothesis ... |
| nfsbc1v 3699 | Bound-variable hypothesis ... |
| nfsbcdw 3700 | Deduction version of ~ nfs... |
| nfsbcw 3701 | Bound-variable hypothesis ... |
| sbccow 3702 | A composition law for clas... |
| nfsbcd 3703 | Deduction version of ~ nfs... |
| nfsbc 3704 | Bound-variable hypothesis ... |
| sbcco 3705 | A composition law for clas... |
| sbcco2 3706 | A composition law for clas... |
| sbc5 3707 | An equivalence for class s... |
| sbc5ALT 3708 | Alternate proof of ~ sbc5 ... |
| sbc6g 3709 | An equivalence for class s... |
| sbc6 3710 | An equivalence for class s... |
| sbc7 3711 | An equivalence for class s... |
| cbvsbcw 3712 | Change bound variables in ... |
| cbvsbcvw 3713 | Change the bound variable ... |
| cbvsbc 3714 | Change bound variables in ... |
| cbvsbcv 3715 | Change the bound variable ... |
| sbciegft 3716 | Conversion of implicit sub... |
| sbciegf 3717 | Conversion of implicit sub... |
| sbcieg 3718 | Conversion of implicit sub... |
| sbcie2g 3719 | Conversion of implicit sub... |
| sbcie 3720 | Conversion of implicit sub... |
| sbciedf 3721 | Conversion of implicit sub... |
| sbcied 3722 | Conversion of implicit sub... |
| sbcied2 3723 | Conversion of implicit sub... |
| elrabsf 3724 | Membership in a restricted... |
| eqsbc3 3725 | Substitution applied to an... |
| sbcng 3726 | Move negation in and out o... |
| sbcimg 3727 | Distribution of class subs... |
| sbcan 3728 | Distribution of class subs... |
| sbcor 3729 | Distribution of class subs... |
| sbcbig 3730 | Distribution of class subs... |
| sbcn1 3731 | Move negation in and out o... |
| sbcim1 3732 | Distribution of class subs... |
| sbcbid 3733 | Formula-building deduction... |
| sbcbidv 3734 | Formula-building deduction... |
| sbcbidvOLD 3735 | Obsolete version of ~ sbcb... |
| sbcbii 3736 | Formula-building inference... |
| sbcbi1 3737 | Distribution of class subs... |
| sbcbi2 3738 | Substituting into equivale... |
| sbcbi2OLD 3739 | Obsolete proof of ~ sbcbi2... |
| sbcal 3740 | Move universal quantifier ... |
| sbcex2 3741 | Move existential quantifie... |
| sbceqal 3742 | Class version of one impli... |
| sbeqalb 3743 | Theorem *14.121 in [Whiteh... |
| eqsbc3r 3744 | ~ eqsbc3 with setvar varia... |
| sbc3an 3745 | Distribution of class subs... |
| sbcel1v 3746 | Class substitution into a ... |
| sbcel2gv 3747 | Class substitution into a ... |
| sbcel21v 3748 | Class substitution into a ... |
| sbcimdv 3749 | Substitution analogue of T... |
| sbctt 3750 | Substitution for a variabl... |
| sbcgf 3751 | Substitution for a variabl... |
| sbc19.21g 3752 | Substitution for a variabl... |
| sbcg 3753 | Substitution for a variabl... |
| sbcgfi 3754 | Substitution for a variabl... |
| sbc2iegf 3755 | Conversion of implicit sub... |
| sbc2ie 3756 | Conversion of implicit sub... |
| sbc2iedv 3757 | Conversion of implicit sub... |
| sbc3ie 3758 | Conversion of implicit sub... |
| sbccomlem 3759 | Lemma for ~ sbccom . (Con... |
| sbccom 3760 | Commutative law for double... |
| sbcralt 3761 | Interchange class substitu... |
| sbcrext 3762 | Interchange class substitu... |
| sbcralg 3763 | Interchange class substitu... |
| sbcrex 3764 | Interchange class substitu... |
| sbcreu 3765 | Interchange class substitu... |
| reu8nf 3766 | Restricted uniqueness usin... |
| sbcabel 3767 | Interchange class substitu... |
| rspsbc 3768 | Restricted quantifier vers... |
| rspsbca 3769 | Restricted quantifier vers... |
| rspesbca 3770 | Existence form of ~ rspsbc... |
| spesbc 3771 | Existence form of ~ spsbc ... |
| spesbcd 3772 | form of ~ spsbc . (Contri... |
| sbcth2 3773 | A substitution into a theo... |
| ra4v 3774 | Version of ~ ra4 with a di... |
| ra4 3775 | Restricted quantifier vers... |
| rmo2 3776 | Alternate definition of re... |
| rmo2i 3777 | Condition implying restric... |
| rmo3 3778 | Restricted "at most one" u... |
| rmob 3779 | Consequence of "at most on... |
| rmoi 3780 | Consequence of "at most on... |
| rmob2 3781 | Consequence of "restricted... |
| rmoi2 3782 | Consequence of "restricted... |
| rmoanim 3783 | Introduction of a conjunct... |
| rmoanimALT 3784 | Alternate proof of ~ rmoan... |
| reuan 3785 | Introduction of a conjunct... |
| 2reu1 3786 | Double restricted existent... |
| 2reu2 3787 | Double restricted existent... |
| csb2 3790 | Alternate expression for t... |
| csbeq1 3791 | Analogue of ~ dfsbcq for p... |
| csbeq1d 3792 | Equality deduction for pro... |
| csbeq2 3793 | Substituting into equivale... |
| csbeq2d 3794 | Formula-building deduction... |
| csbeq2dv 3795 | Formula-building deduction... |
| csbeq2i 3796 | Formula-building inference... |
| csbeq12dv 3797 | Formula-building inference... |
| cbvcsbw 3798 | Change bound variables in ... |
| cbvcsb 3799 | Change bound variables in ... |
| cbvcsbv 3800 | Change the bound variable ... |
| csbid 3801 | Analogue of ~ sbid for pro... |
| csbeq1a 3802 | Equality theorem for prope... |
| csbcow 3803 | Composition law for chaine... |
| csbco 3804 | Composition law for chaine... |
| csbtt 3805 | Substitution doesn't affec... |
| csbconstgf 3806 | Substitution doesn't affec... |
| csbconstg 3807 | Substitution doesn't affec... |
| csbgfi 3808 | Substitution for a variabl... |
| csbconstgi 3809 | The proper substitution of... |
| nfcsb1d 3810 | Bound-variable hypothesis ... |
| nfcsb1 3811 | Bound-variable hypothesis ... |
| nfcsb1v 3812 | Bound-variable hypothesis ... |
| nfcsbd 3813 | Deduction version of ~ nfc... |
| nfcsbw 3814 | Bound-variable hypothesis ... |
| nfcsb 3815 | Bound-variable hypothesis ... |
| csbhypf 3816 | Introduce an explicit subs... |
| csbiebt 3817 | Conversion of implicit sub... |
| csbiedf 3818 | Conversion of implicit sub... |
| csbieb 3819 | Bidirectional conversion b... |
| csbiebg 3820 | Bidirectional conversion b... |
| csbiegf 3821 | Conversion of implicit sub... |
| csbief 3822 | Conversion of implicit sub... |
| csbie 3823 | Conversion of implicit sub... |
| csbied 3824 | Conversion of implicit sub... |
| csbied2 3825 | Conversion of implicit sub... |
| csbie2t 3826 | Conversion of implicit sub... |
| csbie2 3827 | Conversion of implicit sub... |
| csbie2g 3828 | Conversion of implicit sub... |
| cbvrabcsfw 3829 | Version of ~ cbvrabcsf wit... |
| cbvralcsf 3830 | A more general version of ... |
| cbvrexcsf 3831 | A more general version of ... |
| cbvreucsf 3832 | A more general version of ... |
| cbvrabcsf 3833 | A more general version of ... |
| cbvralv2 3834 | Rule used to change the bo... |
| cbvrexv2 3835 | Rule used to change the bo... |
| vtocl2dOLD 3836 | Obsolete version of ~ vtoc... |
| rspc2vd 3837 | Deduction version of 2-var... |
| difjust 3843 | Soundness justification th... |
| unjust 3845 | Soundness justification th... |
| injust 3847 | Soundness justification th... |
| dfin5 3849 | Alternate definition for t... |
| dfdif2 3850 | Alternate definition of cl... |
| eldif 3851 | Expansion of membership in... |
| eldifd 3852 | If a class is in one class... |
| eldifad 3853 | If a class is in the diffe... |
| eldifbd 3854 | If a class is in the diffe... |
| elneeldif 3855 | The elements of a set diff... |
| velcomp 3856 | Characterization of setvar... |
| elin 3857 | Expansion of membership in... |
| dfss 3859 | Variant of subclass defini... |
| dfss2 3861 | Alternate definition of th... |
| dfss2OLD 3862 | Obsolete version of ~ dfss... |
| dfss3 3863 | Alternate definition of su... |
| dfss6 3864 | Alternate definition of su... |
| dfss2f 3865 | Equivalence for subclass r... |
| dfss3f 3866 | Equivalence for subclass r... |
| nfss 3867 | If ` x ` is not free in ` ... |
| ssel 3868 | Membership relationships f... |
| sselOLD 3869 | Obsolete version of ~ ssel... |
| ssel2 3870 | Membership relationships f... |
| sseli 3871 | Membership implication fro... |
| sselii 3872 | Membership inference from ... |
| sseldi 3873 | Membership inference from ... |
| sseld 3874 | Membership deduction from ... |
| sselda 3875 | Membership deduction from ... |
| sseldd 3876 | Membership inference from ... |
| ssneld 3877 | If a class is not in anoth... |
| ssneldd 3878 | If an element is not in a ... |
| ssriv 3879 | Inference based on subclas... |
| ssrd 3880 | Deduction based on subclas... |
| ssrdv 3881 | Deduction based on subclas... |
| sstr2 3882 | Transitivity of subclass r... |
| sstr 3883 | Transitivity of subclass r... |
| sstri 3884 | Subclass transitivity infe... |
| sstrd 3885 | Subclass transitivity dedu... |
| sstrid 3886 | Subclass transitivity dedu... |
| sstrdi 3887 | Subclass transitivity dedu... |
| sylan9ss 3888 | A subclass transitivity de... |
| sylan9ssr 3889 | A subclass transitivity de... |
| eqss 3890 | The subclass relationship ... |
| eqssi 3891 | Infer equality from two su... |
| eqssd 3892 | Equality deduction from tw... |
| sssseq 3893 | If a class is a subclass o... |
| eqrd 3894 | Deduce equality of classes... |
| eqri 3895 | Infer equality of classes ... |
| eqelssd 3896 | Equality deduction from su... |
| ssid 3897 | Any class is a subclass of... |
| ssidd 3898 | Weakening of ~ ssid . (Co... |
| ssv 3899 | Any class is a subclass of... |
| sseq1 3900 | Equality theorem for subcl... |
| sseq2 3901 | Equality theorem for the s... |
| sseq12 3902 | Equality theorem for the s... |
| sseq1i 3903 | An equality inference for ... |
| sseq2i 3904 | An equality inference for ... |
| sseq12i 3905 | An equality inference for ... |
| sseq1d 3906 | An equality deduction for ... |
| sseq2d 3907 | An equality deduction for ... |
| sseq12d 3908 | An equality deduction for ... |
| eqsstri 3909 | Substitution of equality i... |
| eqsstrri 3910 | Substitution of equality i... |
| sseqtri 3911 | Substitution of equality i... |
| sseqtrri 3912 | Substitution of equality i... |
| eqsstrd 3913 | Substitution of equality i... |
| eqsstrrd 3914 | Substitution of equality i... |
| sseqtrd 3915 | Substitution of equality i... |
| sseqtrrd 3916 | Substitution of equality i... |
| 3sstr3i 3917 | Substitution of equality i... |
| 3sstr4i 3918 | Substitution of equality i... |
| 3sstr3g 3919 | Substitution of equality i... |
| 3sstr4g 3920 | Substitution of equality i... |
| 3sstr3d 3921 | Substitution of equality i... |
| 3sstr4d 3922 | Substitution of equality i... |
| eqsstrid 3923 | A chained subclass and equ... |
| eqsstrrid 3924 | A chained subclass and equ... |
| sseqtrdi 3925 | A chained subclass and equ... |
| sseqtrrdi 3926 | A chained subclass and equ... |
| sseqtrid 3927 | Subclass transitivity dedu... |
| sseqtrrid 3928 | Subclass transitivity dedu... |
| eqsstrdi 3929 | A chained subclass and equ... |
| eqsstrrdi 3930 | A chained subclass and equ... |
| eqimss 3931 | Equality implies the subcl... |
| eqimss2 3932 | Equality implies the subcl... |
| eqimssi 3933 | Infer subclass relationshi... |
| eqimss2i 3934 | Infer subclass relationshi... |
| nssne1 3935 | Two classes are different ... |
| nssne2 3936 | Two classes are different ... |
| nss 3937 | Negation of subclass relat... |
| nelss 3938 | Demonstrate by witnesses t... |
| ssrexf 3939 | Restricted existential qua... |
| ssrmof 3940 | "At most one" existential ... |
| ssralv 3941 | Quantification restricted ... |
| ssrexv 3942 | Existential quantification... |
| ss2ralv 3943 | Two quantifications restri... |
| ss2rexv 3944 | Two existential quantifica... |
| ralss 3945 | Restricted universal quant... |
| rexss 3946 | Restricted existential qua... |
| ss2ab 3947 | Class abstractions in a su... |
| abss 3948 | Class abstraction in a sub... |
| ssab 3949 | Subclass of a class abstra... |
| ssabral 3950 | The relation for a subclas... |
| ss2abdv 3951 | Deduction of abstraction s... |
| ss2abdvALT 3952 | Alternate proof of ~ ss2ab... |
| ss2abdvOLD 3953 | Obsolete version of ~ ss2a... |
| ss2abi 3954 | Inference of abstraction s... |
| ss2abiOLD 3955 | Obsolete version of ~ ss2a... |
| abssdv 3956 | Deduction of abstraction s... |
| abssi 3957 | Inference of abstraction s... |
| ss2rab 3958 | Restricted abstraction cla... |
| rabss 3959 | Restricted class abstracti... |
| ssrab 3960 | Subclass of a restricted c... |
| ssrabdv 3961 | Subclass of a restricted c... |
| rabssdv 3962 | Subclass of a restricted c... |
| ss2rabdv 3963 | Deduction of restricted ab... |
| ss2rabi 3964 | Inference of restricted ab... |
| rabss2 3965 | Subclass law for restricte... |
| ssab2 3966 | Subclass relation for the ... |
| ssrab2 3967 | Subclass relation for a re... |
| ssrab2OLD 3968 | Obsolete version of ~ ssra... |
| ssrab3 3969 | Subclass relation for a re... |
| rabssrabd 3970 | Subclass of a restricted c... |
| ssrabeq 3971 | If the restricting class o... |
| rabssab 3972 | A restricted class is a su... |
| uniiunlem 3973 | A subset relationship usef... |
| dfpss2 3974 | Alternate definition of pr... |
| dfpss3 3975 | Alternate definition of pr... |
| psseq1 3976 | Equality theorem for prope... |
| psseq2 3977 | Equality theorem for prope... |
| psseq1i 3978 | An equality inference for ... |
| psseq2i 3979 | An equality inference for ... |
| psseq12i 3980 | An equality inference for ... |
| psseq1d 3981 | An equality deduction for ... |
| psseq2d 3982 | An equality deduction for ... |
| psseq12d 3983 | An equality deduction for ... |
| pssss 3984 | A proper subclass is a sub... |
| pssne 3985 | Two classes in a proper su... |
| pssssd 3986 | Deduce subclass from prope... |
| pssned 3987 | Proper subclasses are uneq... |
| sspss 3988 | Subclass in terms of prope... |
| pssirr 3989 | Proper subclass is irrefle... |
| pssn2lp 3990 | Proper subclass has no 2-c... |
| sspsstri 3991 | Two ways of stating tricho... |
| ssnpss 3992 | Partial trichotomy law for... |
| psstr 3993 | Transitive law for proper ... |
| sspsstr 3994 | Transitive law for subclas... |
| psssstr 3995 | Transitive law for subclas... |
| psstrd 3996 | Proper subclass inclusion ... |
| sspsstrd 3997 | Transitivity involving sub... |
| psssstrd 3998 | Transitivity involving sub... |
| npss 3999 | A class is not a proper su... |
| ssnelpss 4000 | A subclass missing a membe... |
| ssnelpssd 4001 | Subclass inclusion with on... |
| ssexnelpss 4002 | If there is an element of ... |
| dfdif3 4003 | Alternate definition of cl... |
| difeq1 4004 | Equality theorem for class... |
| difeq2 4005 | Equality theorem for class... |
| difeq12 4006 | Equality theorem for class... |
| difeq1i 4007 | Inference adding differenc... |
| difeq2i 4008 | Inference adding differenc... |
| difeq12i 4009 | Equality inference for cla... |
| difeq1d 4010 | Deduction adding differenc... |
| difeq2d 4011 | Deduction adding differenc... |
| difeq12d 4012 | Equality deduction for cla... |
| difeqri 4013 | Inference from membership ... |
| nfdif 4014 | Bound-variable hypothesis ... |
| eldifi 4015 | Implication of membership ... |
| eldifn 4016 | Implication of membership ... |
| elndif 4017 | A set does not belong to a... |
| neldif 4018 | Implication of membership ... |
| difdif 4019 | Double class difference. ... |
| difss 4020 | Subclass relationship for ... |
| difssd 4021 | A difference of two classe... |
| difss2 4022 | If a class is contained in... |
| difss2d 4023 | If a class is contained in... |
| ssdifss 4024 | Preservation of a subclass... |
| ddif 4025 | Double complement under un... |
| ssconb 4026 | Contraposition law for sub... |
| sscon 4027 | Contraposition law for sub... |
| ssdif 4028 | Difference law for subsets... |
| ssdifd 4029 | If ` A ` is contained in `... |
| sscond 4030 | If ` A ` is contained in `... |
| ssdifssd 4031 | If ` A ` is contained in `... |
| ssdif2d 4032 | If ` A ` is contained in `... |
| raldifb 4033 | Restricted universal quant... |
| rexdifi 4034 | Restricted existential qua... |
| complss 4035 | Complementation reverses i... |
| compleq 4036 | Two classes are equal if a... |
| elun 4037 | Expansion of membership in... |
| elunnel1 4038 | A member of a union that i... |
| uneqri 4039 | Inference from membership ... |
| unidm 4040 | Idempotent law for union o... |
| uncom 4041 | Commutative law for union ... |
| equncom 4042 | If a class equals the unio... |
| equncomi 4043 | Inference form of ~ equnco... |
| uneq1 4044 | Equality theorem for the u... |
| uneq2 4045 | Equality theorem for the u... |
| uneq12 4046 | Equality theorem for the u... |
| uneq1i 4047 | Inference adding union to ... |
| uneq2i 4048 | Inference adding union to ... |
| uneq12i 4049 | Equality inference for the... |
| uneq1d 4050 | Deduction adding union to ... |
| uneq2d 4051 | Deduction adding union to ... |
| uneq12d 4052 | Equality deduction for the... |
| nfun 4053 | Bound-variable hypothesis ... |
| unass 4054 | Associative law for union ... |
| un12 4055 | A rearrangement of union. ... |
| un23 4056 | A rearrangement of union. ... |
| un4 4057 | A rearrangement of the uni... |
| unundi 4058 | Union distributes over its... |
| unundir 4059 | Union distributes over its... |
| ssun1 4060 | Subclass relationship for ... |
| ssun2 4061 | Subclass relationship for ... |
| ssun3 4062 | Subclass law for union of ... |
| ssun4 4063 | Subclass law for union of ... |
| elun1 4064 | Membership law for union o... |
| elun2 4065 | Membership law for union o... |
| elunant 4066 | A statement is true for ev... |
| unss1 4067 | Subclass law for union of ... |
| ssequn1 4068 | A relationship between sub... |
| unss2 4069 | Subclass law for union of ... |
| unss12 4070 | Subclass law for union of ... |
| ssequn2 4071 | A relationship between sub... |
| unss 4072 | The union of two subclasse... |
| unssi 4073 | An inference showing the u... |
| unssd 4074 | A deduction showing the un... |
| unssad 4075 | If ` ( A u. B ) ` is conta... |
| unssbd 4076 | If ` ( A u. B ) ` is conta... |
| ssun 4077 | A condition that implies i... |
| rexun 4078 | Restricted existential qua... |
| ralunb 4079 | Restricted quantification ... |
| ralun 4080 | Restricted quantification ... |
| elini 4081 | Membership in an intersect... |
| elind 4082 | Deduce membership in an in... |
| elinel1 4083 | Membership in an intersect... |
| elinel2 4084 | Membership in an intersect... |
| elin2 4085 | Membership in a class defi... |
| elin1d 4086 | Elementhood in the first s... |
| elin2d 4087 | Elementhood in the first s... |
| elin3 4088 | Membership in a class defi... |
| incom 4089 | Commutative law for inters... |
| incomOLD 4090 | Obsolete version of ~ inco... |
| ineqcom 4091 | Two ways of expressing tha... |
| ineqcomi 4092 | Two ways of expressing tha... |
| ineqri 4093 | Inference from membership ... |
| ineq1 4094 | Equality theorem for inter... |
| ineq2 4095 | Equality theorem for inter... |
| ineq12 4096 | Equality theorem for inter... |
| ineq1i 4097 | Equality inference for int... |
| ineq2i 4098 | Equality inference for int... |
| ineq12i 4099 | Equality inference for int... |
| ineq1d 4100 | Equality deduction for int... |
| ineq2d 4101 | Equality deduction for int... |
| ineq12d 4102 | Equality deduction for int... |
| ineqan12d 4103 | Equality deduction for int... |
| sseqin2 4104 | A relationship between sub... |
| nfin 4105 | Bound-variable hypothesis ... |
| rabbi2dva 4106 | Deduction from a wff to a ... |
| inidm 4107 | Idempotent law for interse... |
| inass 4108 | Associative law for inters... |
| in12 4109 | A rearrangement of interse... |
| in32 4110 | A rearrangement of interse... |
| in13 4111 | A rearrangement of interse... |
| in31 4112 | A rearrangement of interse... |
| inrot 4113 | Rotate the intersection of... |
| in4 4114 | Rearrangement of intersect... |
| inindi 4115 | Intersection distributes o... |
| inindir 4116 | Intersection distributes o... |
| inss1 4117 | The intersection of two cl... |
| inss2 4118 | The intersection of two cl... |
| ssin 4119 | Subclass of intersection. ... |
| ssini 4120 | An inference showing that ... |
| ssind 4121 | A deduction showing that a... |
| ssrin 4122 | Add right intersection to ... |
| sslin 4123 | Add left intersection to s... |
| ssrind 4124 | Add right intersection to ... |
| ss2in 4125 | Intersection of subclasses... |
| ssinss1 4126 | Intersection preserves sub... |
| inss 4127 | Inclusion of an intersecti... |
| rexin 4128 | Restricted existential qua... |
| dfss7 4129 | Alternate definition of su... |
| symdifcom 4132 | Symmetric difference commu... |
| symdifeq1 4133 | Equality theorem for symme... |
| symdifeq2 4134 | Equality theorem for symme... |
| nfsymdif 4135 | Hypothesis builder for sym... |
| elsymdif 4136 | Membership in a symmetric ... |
| dfsymdif4 4137 | Alternate definition of th... |
| elsymdifxor 4138 | Membership in a symmetric ... |
| dfsymdif2 4139 | Alternate definition of th... |
| symdifass 4140 | Symmetric difference is as... |
| difsssymdif 4141 | The symmetric difference c... |
| difsymssdifssd 4142 | If the symmetric differenc... |
| unabs 4143 | Absorption law for union. ... |
| inabs 4144 | Absorption law for interse... |
| nssinpss 4145 | Negation of subclass expre... |
| nsspssun 4146 | Negation of subclass expre... |
| dfss4 4147 | Subclass defined in terms ... |
| dfun2 4148 | An alternate definition of... |
| dfin2 4149 | An alternate definition of... |
| difin 4150 | Difference with intersecti... |
| ssdifim 4151 | Implication of a class dif... |
| ssdifsym 4152 | Symmetric class difference... |
| dfss5 4153 | Alternate definition of su... |
| dfun3 4154 | Union defined in terms of ... |
| dfin3 4155 | Intersection defined in te... |
| dfin4 4156 | Alternate definition of th... |
| invdif 4157 | Intersection with universa... |
| indif 4158 | Intersection with class di... |
| indif2 4159 | Bring an intersection in a... |
| indif1 4160 | Bring an intersection in a... |
| indifcom 4161 | Commutation law for inters... |
| indi 4162 | Distributive law for inter... |
| undi 4163 | Distributive law for union... |
| indir 4164 | Distributive law for inter... |
| undir 4165 | Distributive law for union... |
| unineq 4166 | Infer equality from equali... |
| uneqin 4167 | Equality of union and inte... |
| difundi 4168 | Distributive law for class... |
| difundir 4169 | Distributive law for class... |
| difindi 4170 | Distributive law for class... |
| difindir 4171 | Distributive law for class... |
| indifdi 4172 | Distribute intersection ov... |
| indifdir 4173 | Distribute intersection ov... |
| indifdirOLD 4174 | Obsolete version of ~ indi... |
| difdif2 4175 | Class difference by a clas... |
| undm 4176 | De Morgan's law for union.... |
| indm 4177 | De Morgan's law for inters... |
| difun1 4178 | A relationship involving d... |
| undif3 4179 | An equality involving clas... |
| difin2 4180 | Represent a class differen... |
| dif32 4181 | Swap second and third argu... |
| difabs 4182 | Absorption-like law for cl... |
| sscon34b 4183 | Relative complementation r... |
| rcompleq 4184 | Two subclasses are equal i... |
| dfsymdif3 4185 | Alternate definition of th... |
| unab 4186 | Union of two class abstrac... |
| inab 4187 | Intersection of two class ... |
| difab 4188 | Difference of two class ab... |
| abanssl 4189 | A class abstraction with a... |
| abanssr 4190 | A class abstraction with a... |
| notab 4191 | A class abstraction define... |
| unrab 4192 | Union of two restricted cl... |
| inrab 4193 | Intersection of two restri... |
| inrab2 4194 | Intersection with a restri... |
| difrab 4195 | Difference of two restrict... |
| dfrab3 4196 | Alternate definition of re... |
| dfrab2 4197 | Alternate definition of re... |
| notrab 4198 | Complementation of restric... |
| dfrab3ss 4199 | Restricted class abstracti... |
| rabun2 4200 | Abstraction restricted to ... |
| reuss2 4201 | Transfer uniqueness to a s... |
| reuss 4202 | Transfer uniqueness to a s... |
| reuun1 4203 | Transfer uniqueness to a s... |
| reuun2 4204 | Transfer uniqueness to a s... |
| reupick 4205 | Restricted uniqueness "pic... |
| reupick3 4206 | Restricted uniqueness "pic... |
| reupick2 4207 | Restricted uniqueness "pic... |
| euelss 4208 | Transfer uniqueness of an ... |
| dfnul4 4211 | Alternate definition of th... |
| dfnul2 4212 | Alternate definition of th... |
| dfnul3 4213 | Alternate definition of th... |
| dfnul2OLD 4214 | Obsolete version of ~ dfnu... |
| dfnul3OLD 4215 | Obsolete version of ~ dfnu... |
| dfnul4OLD 4216 | Obsolete version of ~ dfnu... |
| noel 4217 | The empty set has no eleme... |
| noelOLD 4218 | Obsolete version of ~ noel... |
| nel02 4219 | The empty set has no eleme... |
| n0i 4220 | If a class has elements, t... |
| ne0i 4221 | If a class has elements, t... |
| ne0d 4222 | Deduction form of ~ ne0i .... |
| n0ii 4223 | If a class has elements, t... |
| ne0ii 4224 | If a class has elements, t... |
| vn0 4225 | The universal class is not... |
| vn0ALT 4226 | Alternate proof of ~ vn0 .... |
| eq0f 4227 | A class is equal to the em... |
| neq0f 4228 | A class is not empty if an... |
| n0f 4229 | A class is nonempty if and... |
| eq0 4230 | A class is equal to the em... |
| eq0ALT 4231 | Alternate proof of ~ eq0 .... |
| neq0 4232 | A class is not empty if an... |
| n0 4233 | A class is nonempty if and... |
| eq0OLDOLD 4234 | Obsolete version of ~ eq0 ... |
| neq0OLD 4235 | Obsolete version of ~ neq0... |
| n0OLD 4236 | Obsolete version of ~ n0 a... |
| nel0 4237 | From the general negation ... |
| reximdva0 4238 | Restricted existence deduc... |
| rspn0 4239 | Specialization for restric... |
| rspn0OLD 4240 | Obsolete version of ~ rspn... |
| n0rex 4241 | There is an element in a n... |
| ssn0rex 4242 | There is an element in a c... |
| n0moeu 4243 | A case of equivalence of "... |
| rex0 4244 | Vacuous restricted existen... |
| reu0 4245 | Vacuous restricted uniquen... |
| rmo0 4246 | Vacuous restricted at-most... |
| 0el 4247 | Membership of the empty se... |
| n0el 4248 | Negated membership of the ... |
| eqeuel 4249 | A condition which implies ... |
| ssdif0 4250 | Subclass expressed in term... |
| difn0 4251 | If the difference of two s... |
| pssdifn0 4252 | A proper subclass has a no... |
| pssdif 4253 | A proper subclass has a no... |
| ndisj 4254 | Express that an intersecti... |
| difin0ss 4255 | Difference, intersection, ... |
| inssdif0 4256 | Intersection, subclass, an... |
| difid 4257 | The difference between a c... |
| difidALT 4258 | Alternate proof of ~ difid... |
| dif0 4259 | The difference between a c... |
| ab0 4260 | The class of sets verifyin... |
| ab0OLD 4261 | Obsolete version of ~ ab0 ... |
| ab0ALT 4262 | Alternate proof of ~ ab0 ,... |
| dfnf5 4263 | Characterization of nonfre... |
| ab0orv 4264 | The class abstraction defi... |
| ab0orvALT 4265 | Alternate proof of ~ ab0or... |
| abn0 4266 | Nonempty class abstraction... |
| abn0OLD 4267 | Obsolete version of ~ abn0... |
| rab0 4268 | Any restricted class abstr... |
| rabeq0w 4269 | Condition for a restricted... |
| rabeq0 4270 | Condition for a restricted... |
| rabn0 4271 | Nonempty restricted class ... |
| rabxm 4272 | Law of excluded middle, in... |
| rabnc 4273 | Law of noncontradiction, i... |
| elneldisj 4274 | The set of elements ` s ` ... |
| elnelun 4275 | The union of the set of el... |
| un0 4276 | The union of a class with ... |
| in0 4277 | The intersection of a clas... |
| 0un 4278 | The union of the empty set... |
| 0in 4279 | The intersection of the em... |
| inv1 4280 | The intersection of a clas... |
| unv 4281 | The union of a class with ... |
| 0ss 4282 | The null set is a subset o... |
| ss0b 4283 | Any subset of the empty se... |
| ss0 4284 | Any subset of the empty se... |
| sseq0 4285 | A subclass of an empty cla... |
| ssn0 4286 | A class with a nonempty su... |
| 0dif 4287 | The difference between the... |
| abf 4288 | A class abstraction determ... |
| abfOLD 4289 | Obsolete version of ~ abf ... |
| eq0rdv 4290 | Deduction for equality to ... |
| eq0rdvALT 4291 | Alternate proof of ~ eq0rd... |
| csbprc 4292 | The proper substitution of... |
| csb0 4293 | The proper substitution of... |
| csb0OLD 4294 | Obsolete version of ~ csb0... |
| sbcel12 4295 | Distribute proper substitu... |
| sbceqg 4296 | Distribute proper substitu... |
| sbceqi 4297 | Distribution of class subs... |
| sbcnel12g 4298 | Distribute proper substitu... |
| sbcne12 4299 | Distribute proper substitu... |
| sbcel1g 4300 | Move proper substitution i... |
| sbceq1g 4301 | Move proper substitution t... |
| sbcel2 4302 | Move proper substitution i... |
| sbceq2g 4303 | Move proper substitution t... |
| csbcom 4304 | Commutative law for double... |
| sbcnestgfw 4305 | Nest the composition of tw... |
| csbnestgfw 4306 | Nest the composition of tw... |
| sbcnestgw 4307 | Nest the composition of tw... |
| csbnestgw 4308 | Nest the composition of tw... |
| sbcco3gw 4309 | Composition of two substit... |
| sbcnestgf 4310 | Nest the composition of tw... |
| csbnestgf 4311 | Nest the composition of tw... |
| sbcnestg 4312 | Nest the composition of tw... |
| csbnestg 4313 | Nest the composition of tw... |
| sbcco3g 4314 | Composition of two substit... |
| csbco3g 4315 | Composition of two class s... |
| csbnest1g 4316 | Nest the composition of tw... |
| csbidm 4317 | Idempotent law for class s... |
| csbvarg 4318 | The proper substitution of... |
| csbvargi 4319 | The proper substitution of... |
| sbccsb 4320 | Substitution into a wff ex... |
| sbccsb2 4321 | Substitution into a wff ex... |
| rspcsbela 4322 | Special case related to ~ ... |
| sbnfc2 4323 | Two ways of expressing " `... |
| csbab 4324 | Move substitution into a c... |
| csbun 4325 | Distribution of class subs... |
| csbin 4326 | Distribute proper substitu... |
| csbie2df 4327 | Conversion of implicit sub... |
| 2nreu 4328 | If there are two different... |
| un00 4329 | Two classes are empty iff ... |
| vss 4330 | Only the universal class h... |
| 0pss 4331 | The null set is a proper s... |
| npss0 4332 | No set is a proper subset ... |
| pssv 4333 | Any non-universal class is... |
| disj 4334 | Two ways of saying that tw... |
| disjOLD 4335 | Obsolete version of ~ disj... |
| disjr 4336 | Two ways of saying that tw... |
| disj1 4337 | Two ways of saying that tw... |
| reldisj 4338 | Two ways of saying that tw... |
| reldisjOLD 4339 | Obsolete version of ~ reld... |
| disj3 4340 | Two ways of saying that tw... |
| disjne 4341 | Members of disjoint sets a... |
| disjeq0 4342 | Two disjoint sets are equa... |
| disjel 4343 | A set can't belong to both... |
| disj2 4344 | Two ways of saying that tw... |
| disj4 4345 | Two ways of saying that tw... |
| ssdisj 4346 | Intersection with a subcla... |
| disjpss 4347 | A class is a proper subset... |
| undisj1 4348 | The union of disjoint clas... |
| undisj2 4349 | The union of disjoint clas... |
| ssindif0 4350 | Subclass expressed in term... |
| inelcm 4351 | The intersection of classe... |
| minel 4352 | A minimum element of a cla... |
| undif4 4353 | Distribute union over diff... |
| disjssun 4354 | Subset relation for disjoi... |
| vdif0 4355 | Universal class equality i... |
| difrab0eq 4356 | If the difference between ... |
| pssnel 4357 | A proper subclass has a me... |
| disjdif 4358 | A class and its relative c... |
| disjdifr 4359 | A class and its relative c... |
| difin0 4360 | The difference of a class ... |
| unvdif 4361 | The union of a class and i... |
| undif1 4362 | Absorption of difference b... |
| undif2 4363 | Absorption of difference b... |
| undifabs 4364 | Absorption of difference b... |
| inundif 4365 | The intersection and class... |
| disjdif2 4366 | The difference of a class ... |
| difun2 4367 | Absorption of union by dif... |
| undif 4368 | Union of complementary par... |
| ssdifin0 4369 | A subset of a difference d... |
| ssdifeq0 4370 | A class is a subclass of i... |
| ssundif 4371 | A condition equivalent to ... |
| difcom 4372 | Swap the arguments of a cl... |
| pssdifcom1 4373 | Two ways to express overla... |
| pssdifcom2 4374 | Two ways to express non-co... |
| difdifdir 4375 | Distributive law for class... |
| uneqdifeq 4376 | Two ways to say that ` A `... |
| raldifeq 4377 | Equality theorem for restr... |
| r19.2z 4378 | Theorem 19.2 of [Margaris]... |
| r19.2zb 4379 | A response to the notion t... |
| r19.3rz 4380 | Restricted quantification ... |
| r19.28z 4381 | Restricted quantifier vers... |
| r19.3rzv 4382 | Restricted quantification ... |
| r19.9rzv 4383 | Restricted quantification ... |
| r19.28zv 4384 | Restricted quantifier vers... |
| r19.37zv 4385 | Restricted quantifier vers... |
| r19.45zv 4386 | Restricted version of Theo... |
| r19.44zv 4387 | Restricted version of Theo... |
| r19.27z 4388 | Restricted quantifier vers... |
| r19.27zv 4389 | Restricted quantifier vers... |
| r19.36zv 4390 | Restricted quantifier vers... |
| ralidmw 4391 | Idempotent law for restric... |
| rzal 4392 | Vacuous quantification is ... |
| rzalALT 4393 | Alternate proof of ~ rzal ... |
| rexn0 4394 | Restricted existential qua... |
| ralidm 4395 | Idempotent law for restric... |
| ral0 4396 | Vacuous universal quantifi... |
| ralf0 4397 | The quantification of a fa... |
| rexn0OLD 4398 | Obsolete version of ~ rexn... |
| ralidmOLD 4399 | Obsolete version of ~ rali... |
| ral0OLD 4400 | Obsolete version of ~ ral0... |
| ralf0OLD 4401 | Obsolete version of ~ ralf... |
| ralnralall 4402 | A contradiction concerning... |
| falseral0 4403 | A false statement can only... |
| raaan 4404 | Rearrange restricted quant... |
| raaanv 4405 | Rearrange restricted quant... |
| sbss 4406 | Set substitution into the ... |
| sbcssg 4407 | Distribute proper substitu... |
| raaan2 4408 | Rearrange restricted quant... |
| 2reu4lem 4409 | Lemma for ~ 2reu4 . (Cont... |
| 2reu4 4410 | Definition of double restr... |
| dfif2 4413 | An alternate definition of... |
| dfif6 4414 | An alternate definition of... |
| ifeq1 4415 | Equality theorem for condi... |
| ifeq2 4416 | Equality theorem for condi... |
| iftrue 4417 | Value of the conditional o... |
| iftruei 4418 | Inference associated with ... |
| iftrued 4419 | Value of the conditional o... |
| iffalse 4420 | Value of the conditional o... |
| iffalsei 4421 | Inference associated with ... |
| iffalsed 4422 | Value of the conditional o... |
| ifnefalse 4423 | When values are unequal, b... |
| ifsb 4424 | Distribute a function over... |
| dfif3 4425 | Alternate definition of th... |
| dfif4 4426 | Alternate definition of th... |
| dfif5 4427 | Alternate definition of th... |
| ifssun 4428 | A conditional class is inc... |
| ifeq12 4429 | Equality theorem for condi... |
| ifeq1d 4430 | Equality deduction for con... |
| ifeq2d 4431 | Equality deduction for con... |
| ifeq12d 4432 | Equality deduction for con... |
| ifbi 4433 | Equivalence theorem for co... |
| ifbid 4434 | Equivalence deduction for ... |
| ifbieq1d 4435 | Equivalence/equality deduc... |
| ifbieq2i 4436 | Equivalence/equality infer... |
| ifbieq2d 4437 | Equivalence/equality deduc... |
| ifbieq12i 4438 | Equivalence deduction for ... |
| ifbieq12d 4439 | Equivalence deduction for ... |
| nfifd 4440 | Deduction form of ~ nfif .... |
| nfif 4441 | Bound-variable hypothesis ... |
| ifeq1da 4442 | Conditional equality. (Co... |
| ifeq2da 4443 | Conditional equality. (Co... |
| ifeq12da 4444 | Equivalence deduction for ... |
| ifbieq12d2 4445 | Equivalence deduction for ... |
| ifclda 4446 | Conditional closure. (Con... |
| ifeqda 4447 | Separation of the values o... |
| elimif 4448 | Elimination of a condition... |
| ifbothda 4449 | A wff ` th ` containing a ... |
| ifboth 4450 | A wff ` th ` containing a ... |
| ifid 4451 | Identical true and false a... |
| eqif 4452 | Expansion of an equality w... |
| ifval 4453 | Another expression of the ... |
| elif 4454 | Membership in a conditiona... |
| ifel 4455 | Membership of a conditiona... |
| ifcl 4456 | Membership (closure) of a ... |
| ifcld 4457 | Membership (closure) of a ... |
| ifcli 4458 | Inference associated with ... |
| ifexd 4459 | Existence of the condition... |
| ifexg 4460 | Existence of the condition... |
| ifex 4461 | Existence of the condition... |
| ifeqor 4462 | The possible values of a c... |
| ifnot 4463 | Negating the first argumen... |
| ifan 4464 | Rewrite a conjunction in a... |
| ifor 4465 | Rewrite a disjunction in a... |
| 2if2 4466 | Resolve two nested conditi... |
| ifcomnan 4467 | Commute the conditions in ... |
| csbif 4468 | Distribute proper substitu... |
| dedth 4469 | Weak deduction theorem tha... |
| dedth2h 4470 | Weak deduction theorem eli... |
| dedth3h 4471 | Weak deduction theorem eli... |
| dedth4h 4472 | Weak deduction theorem eli... |
| dedth2v 4473 | Weak deduction theorem for... |
| dedth3v 4474 | Weak deduction theorem for... |
| dedth4v 4475 | Weak deduction theorem for... |
| elimhyp 4476 | Eliminate a hypothesis con... |
| elimhyp2v 4477 | Eliminate a hypothesis con... |
| elimhyp3v 4478 | Eliminate a hypothesis con... |
| elimhyp4v 4479 | Eliminate a hypothesis con... |
| elimel 4480 | Eliminate a membership hyp... |
| elimdhyp 4481 | Version of ~ elimhyp where... |
| keephyp 4482 | Transform a hypothesis ` p... |
| keephyp2v 4483 | Keep a hypothesis containi... |
| keephyp3v 4484 | Keep a hypothesis containi... |
| pwjust 4486 | Soundness justification th... |
| elpwg 4488 | Membership in a power clas... |
| elpw 4489 | Membership in a power clas... |
| velpw 4490 | Setvar variable membership... |
| elpwOLD 4491 | Obsolete proof of ~ elpw a... |
| elpwgOLD 4492 | Obsolete proof of ~ elpwg ... |
| elpwd 4493 | Membership in a power clas... |
| elpwi 4494 | Subset relation implied by... |
| elpwb 4495 | Characterization of the el... |
| elpwid 4496 | An element of a power clas... |
| elelpwi 4497 | If ` A ` belongs to a part... |
| sspw 4498 | The powerclass preserves i... |
| sspwi 4499 | The powerclass preserves i... |
| sspwd 4500 | The powerclass preserves i... |
| pweq 4501 | Equality theorem for power... |
| pweqALT 4502 | Alternate proof of ~ pweq ... |
| pweqi 4503 | Equality inference for pow... |
| pweqd 4504 | Equality deduction for pow... |
| pwunss 4505 | The power class of the uni... |
| nfpw 4506 | Bound-variable hypothesis ... |
| pwidg 4507 | A set is an element of its... |
| pwidb 4508 | A class is an element of i... |
| pwid 4509 | A set is a member of its p... |
| pwss 4510 | Subclass relationship for ... |
| pwundif 4511 | Break up the power class o... |
| snjust 4512 | Soundness justification th... |
| sneq 4523 | Equality theorem for singl... |
| sneqi 4524 | Equality inference for sin... |
| sneqd 4525 | Equality deduction for sin... |
| dfsn2 4526 | Alternate definition of si... |
| elsng 4527 | There is exactly one eleme... |
| elsn 4528 | There is exactly one eleme... |
| velsn 4529 | There is only one element ... |
| elsni 4530 | There is at most one eleme... |
| absn 4531 | Condition for a class abst... |
| dfpr2 4532 | Alternate definition of a ... |
| dfsn2ALT 4533 | Alternate definition of si... |
| elprg 4534 | A member of a pair of clas... |
| elpri 4535 | If a class is an element o... |
| elpr 4536 | A member of a pair of clas... |
| elpr2g 4537 | A member of a pair of sets... |
| elpr2 4538 | A member of a pair of sets... |
| elpr2OLD 4539 | Obsolete version of ~ elpr... |
| nelpr2 4540 | If a class is not an eleme... |
| nelpr1 4541 | If a class is not an eleme... |
| nelpri 4542 | If an element doesn't matc... |
| prneli 4543 | If an element doesn't matc... |
| nelprd 4544 | If an element doesn't matc... |
| eldifpr 4545 | Membership in a set with t... |
| rexdifpr 4546 | Restricted existential qua... |
| snidg 4547 | A set is a member of its s... |
| snidb 4548 | A class is a set iff it is... |
| snid 4549 | A set is a member of its s... |
| vsnid 4550 | A setvar variable is a mem... |
| elsn2g 4551 | There is exactly one eleme... |
| elsn2 4552 | There is exactly one eleme... |
| nelsn 4553 | If a class is not equal to... |
| rabeqsn 4554 | Conditions for a restricte... |
| rabsssn 4555 | Conditions for a restricte... |
| ralsnsg 4556 | Substitution expressed in ... |
| rexsns 4557 | Restricted existential qua... |
| rexsngf 4558 | Restricted existential qua... |
| ralsngf 4559 | Restricted universal quant... |
| reusngf 4560 | Restricted existential uni... |
| ralsng 4561 | Substitution expressed in ... |
| rexsng 4562 | Restricted existential qua... |
| reusng 4563 | Restricted existential uni... |
| 2ralsng 4564 | Substitution expressed in ... |
| ralsngOLD 4565 | Obsolete version of ~ rals... |
| rexsngOLD 4566 | Obsolete version of ~ rexs... |
| rexreusng 4567 | Restricted existential uni... |
| exsnrex 4568 | There is a set being the e... |
| ralsn 4569 | Convert a universal quanti... |
| rexsn 4570 | Convert an existential qua... |
| elpwunsn 4571 | Membership in an extension... |
| eqoreldif 4572 | An element of a set is eit... |
| eltpg 4573 | Members of an unordered tr... |
| eldiftp 4574 | Membership in a set with t... |
| eltpi 4575 | A member of an unordered t... |
| eltp 4576 | A member of an unordered t... |
| dftp2 4577 | Alternate definition of un... |
| nfpr 4578 | Bound-variable hypothesis ... |
| ifpr 4579 | Membership of a conditiona... |
| ralprgf 4580 | Convert a restricted unive... |
| rexprgf 4581 | Convert a restricted exist... |
| ralprg 4582 | Convert a restricted unive... |
| ralprgOLD 4583 | Obsolete version of ~ ralp... |
| rexprg 4584 | Convert a restricted exist... |
| rexprgOLD 4585 | Obsolete version of ~ rexp... |
| raltpg 4586 | Convert a restricted unive... |
| rextpg 4587 | Convert a restricted exist... |
| ralpr 4588 | Convert a restricted unive... |
| rexpr 4589 | Convert a restricted exist... |
| reuprg0 4590 | Convert a restricted exist... |
| reuprg 4591 | Convert a restricted exist... |
| reurexprg 4592 | Convert a restricted exist... |
| raltp 4593 | Convert a universal quanti... |
| rextp 4594 | Convert an existential qua... |
| nfsn 4595 | Bound-variable hypothesis ... |
| csbsng 4596 | Distribute proper substitu... |
| csbprg 4597 | Distribute proper substitu... |
| elinsn 4598 | If the intersection of two... |
| disjsn 4599 | Intersection with the sing... |
| disjsn2 4600 | Two distinct singletons ar... |
| disjpr2 4601 | Two completely distinct un... |
| disjprsn 4602 | The disjoint intersection ... |
| disjtpsn 4603 | The disjoint intersection ... |
| disjtp2 4604 | Two completely distinct un... |
| snprc 4605 | The singleton of a proper ... |
| snnzb 4606 | A singleton is nonempty if... |
| rmosn 4607 | A restricted at-most-one q... |
| r19.12sn 4608 | Special case of ~ r19.12 w... |
| rabsn 4609 | Condition where a restrict... |
| rabsnifsb 4610 | A restricted class abstrac... |
| rabsnif 4611 | A restricted class abstrac... |
| rabrsn 4612 | A restricted class abstrac... |
| euabsn2 4613 | Another way to express exi... |
| euabsn 4614 | Another way to express exi... |
| reusn 4615 | A way to express restricte... |
| absneu 4616 | Restricted existential uni... |
| rabsneu 4617 | Restricted existential uni... |
| eusn 4618 | Two ways to express " ` A ... |
| rabsnt 4619 | Truth implied by equality ... |
| prcom 4620 | Commutative law for unorde... |
| preq1 4621 | Equality theorem for unord... |
| preq2 4622 | Equality theorem for unord... |
| preq12 4623 | Equality theorem for unord... |
| preq1i 4624 | Equality inference for uno... |
| preq2i 4625 | Equality inference for uno... |
| preq12i 4626 | Equality inference for uno... |
| preq1d 4627 | Equality deduction for uno... |
| preq2d 4628 | Equality deduction for uno... |
| preq12d 4629 | Equality deduction for uno... |
| tpeq1 4630 | Equality theorem for unord... |
| tpeq2 4631 | Equality theorem for unord... |
| tpeq3 4632 | Equality theorem for unord... |
| tpeq1d 4633 | Equality theorem for unord... |
| tpeq2d 4634 | Equality theorem for unord... |
| tpeq3d 4635 | Equality theorem for unord... |
| tpeq123d 4636 | Equality theorem for unord... |
| tprot 4637 | Rotation of the elements o... |
| tpcoma 4638 | Swap 1st and 2nd members o... |
| tpcomb 4639 | Swap 2nd and 3rd members o... |
| tpass 4640 | Split off the first elemen... |
| qdass 4641 | Two ways to write an unord... |
| qdassr 4642 | Two ways to write an unord... |
| tpidm12 4643 | Unordered triple ` { A , A... |
| tpidm13 4644 | Unordered triple ` { A , B... |
| tpidm23 4645 | Unordered triple ` { A , B... |
| tpidm 4646 | Unordered triple ` { A , A... |
| tppreq3 4647 | An unordered triple is an ... |
| prid1g 4648 | An unordered pair contains... |
| prid2g 4649 | An unordered pair contains... |
| prid1 4650 | An unordered pair contains... |
| prid2 4651 | An unordered pair contains... |
| ifpprsnss 4652 | An unordered pair is a sin... |
| prprc1 4653 | A proper class vanishes in... |
| prprc2 4654 | A proper class vanishes in... |
| prprc 4655 | An unordered pair containi... |
| tpid1 4656 | One of the three elements ... |
| tpid1g 4657 | Closed theorem form of ~ t... |
| tpid2 4658 | One of the three elements ... |
| tpid2g 4659 | Closed theorem form of ~ t... |
| tpid3g 4660 | Closed theorem form of ~ t... |
| tpid3 4661 | One of the three elements ... |
| snnzg 4662 | The singleton of a set is ... |
| snn0d 4663 | The singleton of a set is ... |
| snnz 4664 | The singleton of a set is ... |
| prnz 4665 | A pair containing a set is... |
| prnzg 4666 | A pair containing a set is... |
| tpnz 4667 | An unordered triple contai... |
| tpnzd 4668 | An unordered triple contai... |
| raltpd 4669 | Convert a universal quanti... |
| snssg 4670 | The singleton of an elemen... |
| snss 4671 | The singleton of an elemen... |
| eldifsn 4672 | Membership in a set with a... |
| ssdifsn 4673 | Subset of a set with an el... |
| elpwdifsn 4674 | A subset of a set is an el... |
| eldifsni 4675 | Membership in a set with a... |
| eldifsnneq 4676 | An element of a difference... |
| neldifsn 4677 | The class ` A ` is not in ... |
| neldifsnd 4678 | The class ` A ` is not in ... |
| rexdifsn 4679 | Restricted existential qua... |
| raldifsni 4680 | Rearrangement of a propert... |
| raldifsnb 4681 | Restricted universal quant... |
| eldifvsn 4682 | A set is an element of the... |
| difsn 4683 | An element not in a set ca... |
| difprsnss 4684 | Removal of a singleton fro... |
| difprsn1 4685 | Removal of a singleton fro... |
| difprsn2 4686 | Removal of a singleton fro... |
| diftpsn3 4687 | Removal of a singleton fro... |
| difpr 4688 | Removing two elements as p... |
| tpprceq3 4689 | An unordered triple is an ... |
| tppreqb 4690 | An unordered triple is an ... |
| difsnb 4691 | ` ( B \ { A } ) ` equals `... |
| difsnpss 4692 | ` ( B \ { A } ) ` is a pro... |
| snssi 4693 | The singleton of an elemen... |
| snssd 4694 | The singleton of an elemen... |
| difsnid 4695 | If we remove a single elem... |
| eldifeldifsn 4696 | An element of a difference... |
| pw0 4697 | Compute the power set of t... |
| pwpw0 4698 | Compute the power set of t... |
| snsspr1 4699 | A singleton is a subset of... |
| snsspr2 4700 | A singleton is a subset of... |
| snsstp1 4701 | A singleton is a subset of... |
| snsstp2 4702 | A singleton is a subset of... |
| snsstp3 4703 | A singleton is a subset of... |
| prssg 4704 | A pair of elements of a cl... |
| prss 4705 | A pair of elements of a cl... |
| prssi 4706 | A pair of elements of a cl... |
| prssd 4707 | Deduction version of ~ prs... |
| prsspwg 4708 | An unordered pair belongs ... |
| ssprss 4709 | A pair as subset of a pair... |
| ssprsseq 4710 | A proper pair is a subset ... |
| sssn 4711 | The subsets of a singleton... |
| ssunsn2 4712 | The property of being sand... |
| ssunsn 4713 | Possible values for a set ... |
| eqsn 4714 | Two ways to express that a... |
| issn 4715 | A sufficient condition for... |
| n0snor2el 4716 | A nonempty set is either a... |
| ssunpr 4717 | Possible values for a set ... |
| sspr 4718 | The subsets of a pair. (C... |
| sstp 4719 | The subsets of an unordere... |
| tpss 4720 | An unordered triple of ele... |
| tpssi 4721 | An unordered triple of ele... |
| sneqrg 4722 | Closed form of ~ sneqr . ... |
| sneqr 4723 | If the singletons of two s... |
| snsssn 4724 | If a singleton is a subset... |
| mosneq 4725 | There exists at most one s... |
| sneqbg 4726 | Two singletons of sets are... |
| snsspw 4727 | The singleton of a class i... |
| prsspw 4728 | An unordered pair belongs ... |
| preq1b 4729 | Biconditional equality lem... |
| preq2b 4730 | Biconditional equality lem... |
| preqr1 4731 | Reverse equality lemma for... |
| preqr2 4732 | Reverse equality lemma for... |
| preq12b 4733 | Equality relationship for ... |
| opthpr 4734 | An unordered pair has the ... |
| preqr1g 4735 | Reverse equality lemma for... |
| preq12bg 4736 | Closed form of ~ preq12b .... |
| prneimg 4737 | Two pairs are not equal if... |
| prnebg 4738 | A (proper) pair is not equ... |
| pr1eqbg 4739 | A (proper) pair is equal t... |
| pr1nebg 4740 | A (proper) pair is not equ... |
| preqsnd 4741 | Equivalence for a pair equ... |
| prnesn 4742 | A proper unordered pair is... |
| prneprprc 4743 | A proper unordered pair is... |
| preqsn 4744 | Equivalence for a pair equ... |
| preq12nebg 4745 | Equality relationship for ... |
| prel12g 4746 | Equality of two unordered ... |
| opthprneg 4747 | An unordered pair has the ... |
| elpreqprlem 4748 | Lemma for ~ elpreqpr . (C... |
| elpreqpr 4749 | Equality and membership ru... |
| elpreqprb 4750 | A set is an element of an ... |
| elpr2elpr 4751 | For an element ` A ` of an... |
| dfopif 4752 | Rewrite ~ df-op using ` if... |
| dfopifOLD 4753 | Obsolete version of ~ dfop... |
| dfopg 4754 | Value of the ordered pair ... |
| dfop 4755 | Value of an ordered pair w... |
| opeq1 4756 | Equality theorem for order... |
| opeq1OLD 4757 | Obsolete version of ~ opeq... |
| opeq2 4758 | Equality theorem for order... |
| opeq2OLD 4759 | Obsolete version of ~ opeq... |
| opeq12 4760 | Equality theorem for order... |
| opeq1i 4761 | Equality inference for ord... |
| opeq2i 4762 | Equality inference for ord... |
| opeq12i 4763 | Equality inference for ord... |
| opeq1d 4764 | Equality deduction for ord... |
| opeq2d 4765 | Equality deduction for ord... |
| opeq12d 4766 | Equality deduction for ord... |
| oteq1 4767 | Equality theorem for order... |
| oteq2 4768 | Equality theorem for order... |
| oteq3 4769 | Equality theorem for order... |
| oteq1d 4770 | Equality deduction for ord... |
| oteq2d 4771 | Equality deduction for ord... |
| oteq3d 4772 | Equality deduction for ord... |
| oteq123d 4773 | Equality deduction for ord... |
| nfop 4774 | Bound-variable hypothesis ... |
| nfopd 4775 | Deduction version of bound... |
| csbopg 4776 | Distribution of class subs... |
| opidg 4777 | The ordered pair ` <. A , ... |
| opid 4778 | The ordered pair ` <. A , ... |
| ralunsn 4779 | Restricted quantification ... |
| 2ralunsn 4780 | Double restricted quantifi... |
| opprc 4781 | Expansion of an ordered pa... |
| opprc1 4782 | Expansion of an ordered pa... |
| opprc2 4783 | Expansion of an ordered pa... |
| oprcl 4784 | If an ordered pair has an ... |
| pwsn 4785 | The power set of a singlet... |
| pwsnOLD 4786 | Obsolete version of ~ pwsn... |
| pwpr 4787 | The power set of an unorde... |
| pwtp 4788 | The power set of an unorde... |
| pwpwpw0 4789 | Compute the power set of t... |
| pwv 4790 | The power class of the uni... |
| prproe 4791 | For an element of a proper... |
| 3elpr2eq 4792 | If there are three element... |
| dfuni2 4795 | Alternate definition of cl... |
| eluni 4796 | Membership in class union.... |
| eluni2 4797 | Membership in class union.... |
| elunii 4798 | Membership in class union.... |
| nfunid 4799 | Deduction version of ~ nfu... |
| nfuni 4800 | Bound-variable hypothesis ... |
| uniss 4801 | Subclass relationship for ... |
| unissi 4802 | Subclass relationship for ... |
| unissd 4803 | Subclass relationship for ... |
| unieq 4804 | Equality theorem for class... |
| unieqOLD 4805 | Obsolete version of ~ unie... |
| unieqi 4806 | Inference of equality of t... |
| unieqd 4807 | Deduction of equality of t... |
| eluniab 4808 | Membership in union of a c... |
| elunirab 4809 | Membership in union of a c... |
| uniprg 4810 | The union of a pair is the... |
| unipr 4811 | The union of a pair is the... |
| uniprOLD 4812 | Obsolete version of ~ unip... |
| uniprgOLD 4813 | Obsolete version of ~ unip... |
| unisng 4814 | A set equals the union of ... |
| unisn 4815 | A set equals the union of ... |
| unisn3 4816 | Union of a singleton in th... |
| dfnfc2 4817 | An alternative statement o... |
| uniun 4818 | The class union of the uni... |
| uniin 4819 | The class union of the int... |
| ssuni 4820 | Subclass relationship for ... |
| uni0b 4821 | The union of a set is empt... |
| uni0c 4822 | The union of a set is empt... |
| uni0 4823 | The union of the empty set... |
| csbuni 4824 | Distribute proper substitu... |
| elssuni 4825 | An element of a class is a... |
| unissel 4826 | Condition turning a subcla... |
| unissb 4827 | Relationship involving mem... |
| uniss2 4828 | A subclass condition on th... |
| unidif 4829 | If the difference ` A \ B ... |
| ssunieq 4830 | Relationship implying unio... |
| unimax 4831 | Any member of a class is t... |
| pwuni 4832 | A class is a subclass of t... |
| dfint2 4835 | Alternate definition of cl... |
| inteq 4836 | Equality law for intersect... |
| inteqi 4837 | Equality inference for cla... |
| inteqd 4838 | Equality deduction for cla... |
| elint 4839 | Membership in class inters... |
| elint2 4840 | Membership in class inters... |
| elintg 4841 | Membership in class inters... |
| elinti 4842 | Membership in class inters... |
| nfint 4843 | Bound-variable hypothesis ... |
| elintab 4844 | Membership in the intersec... |
| elintrab 4845 | Membership in the intersec... |
| elintrabg 4846 | Membership in the intersec... |
| int0 4847 | The intersection of the em... |
| intss1 4848 | An element of a class incl... |
| ssint 4849 | Subclass of a class inters... |
| ssintab 4850 | Subclass of the intersecti... |
| ssintub 4851 | Subclass of the least uppe... |
| ssmin 4852 | Subclass of the minimum va... |
| intmin 4853 | Any member of a class is t... |
| intss 4854 | Intersection of subclasses... |
| intssuni 4855 | The intersection of a none... |
| ssintrab 4856 | Subclass of the intersecti... |
| unissint 4857 | If the union of a class is... |
| intssuni2 4858 | Subclass relationship for ... |
| intminss 4859 | Under subset ordering, the... |
| intmin2 4860 | Any set is the smallest of... |
| intmin3 4861 | Under subset ordering, the... |
| intmin4 4862 | Elimination of a conjunct ... |
| intab 4863 | The intersection of a spec... |
| int0el 4864 | The intersection of a clas... |
| intun 4865 | The class intersection of ... |
| intprg 4866 | The intersection of a pair... |
| intpr 4867 | The intersection of a pair... |
| intprOLD 4868 | Obsolete version of ~ intp... |
| intprgOLD 4869 | Obsolete version of ~ intp... |
| intsng 4870 | Intersection of a singleto... |
| intsn 4871 | The intersection of a sing... |
| uniintsn 4872 | Two ways to express " ` A ... |
| uniintab 4873 | The union and the intersec... |
| intunsn 4874 | Theorem joining a singleto... |
| rint0 4875 | Relative intersection of a... |
| elrint 4876 | Membership in a restricted... |
| elrint2 4877 | Membership in a restricted... |
| eliun 4882 | Membership in indexed unio... |
| eliin 4883 | Membership in indexed inte... |
| eliuni 4884 | Membership in an indexed u... |
| iuncom 4885 | Commutation of indexed uni... |
| iuncom4 4886 | Commutation of union with ... |
| iunconst 4887 | Indexed union of a constan... |
| iinconst 4888 | Indexed intersection of a ... |
| iuneqconst 4889 | Indexed union of identical... |
| iuniin 4890 | Law combining indexed unio... |
| iinssiun 4891 | An indexed intersection is... |
| iunss1 4892 | Subclass theorem for index... |
| iinss1 4893 | Subclass theorem for index... |
| iuneq1 4894 | Equality theorem for index... |
| iineq1 4895 | Equality theorem for index... |
| ss2iun 4896 | Subclass theorem for index... |
| iuneq2 4897 | Equality theorem for index... |
| iineq2 4898 | Equality theorem for index... |
| iuneq2i 4899 | Equality inference for ind... |
| iineq2i 4900 | Equality inference for ind... |
| iineq2d 4901 | Equality deduction for ind... |
| iuneq2dv 4902 | Equality deduction for ind... |
| iineq2dv 4903 | Equality deduction for ind... |
| iuneq12df 4904 | Equality deduction for ind... |
| iuneq1d 4905 | Equality theorem for index... |
| iuneq12d 4906 | Equality deduction for ind... |
| iuneq2d 4907 | Equality deduction for ind... |
| nfiun 4908 | Bound-variable hypothesis ... |
| nfiin 4909 | Bound-variable hypothesis ... |
| nfiung 4910 | Bound-variable hypothesis ... |
| nfiing 4911 | Bound-variable hypothesis ... |
| nfiu1 4912 | Bound-variable hypothesis ... |
| nfii1 4913 | Bound-variable hypothesis ... |
| dfiun2g 4914 | Alternate definition of in... |
| dfiin2g 4915 | Alternate definition of in... |
| dfiun2 4916 | Alternate definition of in... |
| dfiin2 4917 | Alternate definition of in... |
| dfiunv2 4918 | Define double indexed unio... |
| cbviun 4919 | Rule used to change the bo... |
| cbviin 4920 | Change bound variables in ... |
| cbviung 4921 | Rule used to change the bo... |
| cbviing 4922 | Change bound variables in ... |
| cbviunv 4923 | Rule used to change the bo... |
| cbviinv 4924 | Change bound variables in ... |
| cbviunvg 4925 | Rule used to change the bo... |
| cbviinvg 4926 | Change bound variables in ... |
| iunssf 4927 | Subset theorem for an inde... |
| iunss 4928 | Subset theorem for an inde... |
| ssiun 4929 | Subset implication for an ... |
| ssiun2 4930 | Identity law for subset of... |
| ssiun2s 4931 | Subset relationship for an... |
| iunss2 4932 | A subclass condition on th... |
| iunssd 4933 | Subset theorem for an inde... |
| iunab 4934 | The indexed union of a cla... |
| iunrab 4935 | The indexed union of a res... |
| iunxdif2 4936 | Indexed union with a class... |
| ssiinf 4937 | Subset theorem for an inde... |
| ssiin 4938 | Subset theorem for an inde... |
| iinss 4939 | Subset implication for an ... |
| iinss2 4940 | An indexed intersection is... |
| uniiun 4941 | Class union in terms of in... |
| intiin 4942 | Class intersection in term... |
| iunid 4943 | An indexed union of single... |
| iun0 4944 | An indexed union of the em... |
| 0iun 4945 | An empty indexed union is ... |
| 0iin 4946 | An empty indexed intersect... |
| viin 4947 | Indexed intersection with ... |
| iunsn 4948 | Indexed union of a singlet... |
| iunn0 4949 | There is a nonempty class ... |
| iinab 4950 | Indexed intersection of a ... |
| iinrab 4951 | Indexed intersection of a ... |
| iinrab2 4952 | Indexed intersection of a ... |
| iunin2 4953 | Indexed union of intersect... |
| iunin1 4954 | Indexed union of intersect... |
| iinun2 4955 | Indexed intersection of un... |
| iundif2 4956 | Indexed union of class dif... |
| iindif1 4957 | Indexed intersection of cl... |
| 2iunin 4958 | Rearrange indexed unions o... |
| iindif2 4959 | Indexed intersection of cl... |
| iinin2 4960 | Indexed intersection of in... |
| iinin1 4961 | Indexed intersection of in... |
| iinvdif 4962 | The indexed intersection o... |
| elriin 4963 | Elementhood in a relative ... |
| riin0 4964 | Relative intersection of a... |
| riinn0 4965 | Relative intersection of a... |
| riinrab 4966 | Relative intersection of a... |
| symdif0 4967 | Symmetric difference with ... |
| symdifv 4968 | The symmetric difference w... |
| symdifid 4969 | The symmetric difference o... |
| iinxsng 4970 | A singleton index picks ou... |
| iinxprg 4971 | Indexed intersection with ... |
| iunxsng 4972 | A singleton index picks ou... |
| iunxsn 4973 | A singleton index picks ou... |
| iunxsngf 4974 | A singleton index picks ou... |
| iunun 4975 | Separate a union in an ind... |
| iunxun 4976 | Separate a union in the in... |
| iunxdif3 4977 | An indexed union where som... |
| iunxprg 4978 | A pair index picks out two... |
| iunxiun 4979 | Separate an indexed union ... |
| iinuni 4980 | A relationship involving u... |
| iununi 4981 | A relationship involving u... |
| sspwuni 4982 | Subclass relationship for ... |
| pwssb 4983 | Two ways to express a coll... |
| elpwpw 4984 | Characterization of the el... |
| pwpwab 4985 | The double power class wri... |
| pwpwssunieq 4986 | The class of sets whose un... |
| elpwuni 4987 | Relationship for power cla... |
| iinpw 4988 | The power class of an inte... |
| iunpwss 4989 | Inclusion of an indexed un... |
| intss2 4990 | A nonempty intersection of... |
| rintn0 4991 | Relative intersection of a... |
| dfdisj2 4994 | Alternate definition for d... |
| disjss2 4995 | If each element of a colle... |
| disjeq2 4996 | Equality theorem for disjo... |
| disjeq2dv 4997 | Equality deduction for dis... |
| disjss1 4998 | A subset of a disjoint col... |
| disjeq1 4999 | Equality theorem for disjo... |
| disjeq1d 5000 | Equality theorem for disjo... |
| disjeq12d 5001 | Equality theorem for disjo... |
| cbvdisj 5002 | Change bound variables in ... |
| cbvdisjv 5003 | Change bound variables in ... |
| nfdisjw 5004 | Bound-variable hypothesis ... |
| nfdisj 5005 | Bound-variable hypothesis ... |
| nfdisj1 5006 | Bound-variable hypothesis ... |
| disjor 5007 | Two ways to say that a col... |
| disjors 5008 | Two ways to say that a col... |
| disji2 5009 | Property of a disjoint col... |
| disji 5010 | Property of a disjoint col... |
| invdisj 5011 | If there is a function ` C... |
| invdisjrabw 5012 | Version of ~ invdisjrab wi... |
| invdisjrab 5013 | The restricted class abstr... |
| disjiun 5014 | A disjoint collection yiel... |
| disjord 5015 | Conditions for a collectio... |
| disjiunb 5016 | Two ways to say that a col... |
| disjiund 5017 | Conditions for a collectio... |
| sndisj 5018 | Any collection of singleto... |
| 0disj 5019 | Any collection of empty se... |
| disjxsn 5020 | A singleton collection is ... |
| disjx0 5021 | An empty collection is dis... |
| disjprgw 5022 | Version of ~ disjprg with ... |
| disjprg 5023 | A pair collection is disjo... |
| disjxiun 5024 | An indexed union of a disj... |
| disjxun 5025 | The union of two disjoint ... |
| disjss3 5026 | Expand a disjoint collecti... |
| breq 5029 | Equality theorem for binar... |
| breq1 5030 | Equality theorem for a bin... |
| breq2 5031 | Equality theorem for a bin... |
| breq12 5032 | Equality theorem for a bin... |
| breqi 5033 | Equality inference for bin... |
| breq1i 5034 | Equality inference for a b... |
| breq2i 5035 | Equality inference for a b... |
| breq12i 5036 | Equality inference for a b... |
| breq1d 5037 | Equality deduction for a b... |
| breqd 5038 | Equality deduction for a b... |
| breq2d 5039 | Equality deduction for a b... |
| breq12d 5040 | Equality deduction for a b... |
| breq123d 5041 | Equality deduction for a b... |
| breqdi 5042 | Equality deduction for a b... |
| breqan12d 5043 | Equality deduction for a b... |
| breqan12rd 5044 | Equality deduction for a b... |
| eqnbrtrd 5045 | Substitution of equal clas... |
| nbrne1 5046 | Two classes are different ... |
| nbrne2 5047 | Two classes are different ... |
| eqbrtri 5048 | Substitution of equal clas... |
| eqbrtrd 5049 | Substitution of equal clas... |
| eqbrtrri 5050 | Substitution of equal clas... |
| eqbrtrrd 5051 | Substitution of equal clas... |
| breqtri 5052 | Substitution of equal clas... |
| breqtrd 5053 | Substitution of equal clas... |
| breqtrri 5054 | Substitution of equal clas... |
| breqtrrd 5055 | Substitution of equal clas... |
| 3brtr3i 5056 | Substitution of equality i... |
| 3brtr4i 5057 | Substitution of equality i... |
| 3brtr3d 5058 | Substitution of equality i... |
| 3brtr4d 5059 | Substitution of equality i... |
| 3brtr3g 5060 | Substitution of equality i... |
| 3brtr4g 5061 | Substitution of equality i... |
| eqbrtrid 5062 | A chained equality inferen... |
| eqbrtrrid 5063 | A chained equality inferen... |
| breqtrid 5064 | A chained equality inferen... |
| breqtrrid 5065 | A chained equality inferen... |
| eqbrtrdi 5066 | A chained equality inferen... |
| eqbrtrrdi 5067 | A chained equality inferen... |
| breqtrdi 5068 | A chained equality inferen... |
| breqtrrdi 5069 | A chained equality inferen... |
| ssbrd 5070 | Deduction from a subclass ... |
| ssbr 5071 | Implication from a subclas... |
| ssbri 5072 | Inference from a subclass ... |
| nfbrd 5073 | Deduction version of bound... |
| nfbr 5074 | Bound-variable hypothesis ... |
| brab1 5075 | Relationship between a bin... |
| br0 5076 | The empty binary relation ... |
| brne0 5077 | If two sets are in a binar... |
| brun 5078 | The union of two binary re... |
| brin 5079 | The intersection of two re... |
| brdif 5080 | The difference of two bina... |
| sbcbr123 5081 | Move substitution in and o... |
| sbcbr 5082 | Move substitution in and o... |
| sbcbr12g 5083 | Move substitution in and o... |
| sbcbr1g 5084 | Move substitution in and o... |
| sbcbr2g 5085 | Move substitution in and o... |
| brsymdif 5086 | Characterization of the sy... |
| brralrspcev 5087 | Restricted existential spe... |
| brimralrspcev 5088 | Restricted existential spe... |
| opabss 5091 | The collection of ordered ... |
| opabbid 5092 | Equivalent wff's yield equ... |
| opabbidv 5093 | Equivalent wff's yield equ... |
| opabbii 5094 | Equivalent wff's yield equ... |
| nfopab 5095 | Bound-variable hypothesis ... |
| nfopab1 5096 | The first abstraction vari... |
| nfopab2 5097 | The second abstraction var... |
| cbvopab 5098 | Rule used to change bound ... |
| cbvopabv 5099 | Rule used to change bound ... |
| cbvopab1 5100 | Change first bound variabl... |
| cbvopab1g 5101 | Change first bound variabl... |
| cbvopab2 5102 | Change second bound variab... |
| cbvopab1s 5103 | Change first bound variabl... |
| cbvopab1v 5104 | Rule used to change the fi... |
| cbvopab2v 5105 | Rule used to change the se... |
| unopab 5106 | Union of two ordered pair ... |
| mpteq12df 5109 | An equality inference for ... |
| mpteq12f 5110 | An equality theorem for th... |
| mpteq12dva 5111 | An equality inference for ... |
| mpteq12dv 5112 | An equality inference for ... |
| mpteq12dvOLD 5113 | Obsolete version of ~ mpte... |
| mpteq12 5114 | An equality theorem for th... |
| mpteq1 5115 | An equality theorem for th... |
| mpteq1d 5116 | An equality theorem for th... |
| mpteq1i 5117 | An equality theorem for th... |
| mpteq2ia 5118 | An equality inference for ... |
| mpteq2i 5119 | An equality inference for ... |
| mpteq12i 5120 | An equality inference for ... |
| mpteq2da 5121 | Slightly more general equa... |
| mpteq2dva 5122 | Slightly more general equa... |
| mpteq2dv 5123 | An equality inference for ... |
| nfmpt 5124 | Bound-variable hypothesis ... |
| nfmpt1 5125 | Bound-variable hypothesis ... |
| cbvmptf 5126 | Rule to change the bound v... |
| cbvmptfg 5127 | Rule to change the bound v... |
| cbvmpt 5128 | Rule to change the bound v... |
| cbvmptg 5129 | Rule to change the bound v... |
| cbvmptv 5130 | Rule to change the bound v... |
| cbvmptvg 5131 | Rule to change the bound v... |
| mptv 5132 | Function with universal do... |
| dftr2 5135 | An alternate way of defini... |
| dftr5 5136 | An alternate way of defini... |
| dftr3 5137 | An alternate way of defini... |
| dftr4 5138 | An alternate way of defini... |
| treq 5139 | Equality theorem for the t... |
| trel 5140 | In a transitive class, the... |
| trel3 5141 | In a transitive class, the... |
| trss 5142 | An element of a transitive... |
| trin 5143 | The intersection of transi... |
| tr0 5144 | The empty set is transitiv... |
| trv 5145 | The universe is transitive... |
| triun 5146 | An indexed union of a clas... |
| truni 5147 | The union of a class of tr... |
| triin 5148 | An indexed intersection of... |
| trint 5149 | The intersection of a clas... |
| trintss 5150 | Any nonempty transitive cl... |
| axrep1 5152 | The version of the Axiom o... |
| axreplem 5153 | Lemma for ~ axrep2 and ~ a... |
| axrep2 5154 | Axiom of Replacement expre... |
| axrep3 5155 | Axiom of Replacement sligh... |
| axrep4 5156 | A more traditional version... |
| axrep5 5157 | Axiom of Replacement (simi... |
| axrep6 5158 | A condensed form of ~ ax-r... |
| zfrepclf 5159 | An inference based on the ... |
| zfrep3cl 5160 | An inference based on the ... |
| zfrep4 5161 | A version of Replacement u... |
| axsepgfromrep 5162 | A more general version ~ a... |
| axsep 5163 | Axiom scheme of separation... |
| axsepg 5165 | A more general version of ... |
| zfauscl 5166 | Separation Scheme (Aussond... |
| bm1.3ii 5167 | Convert implication to equ... |
| ax6vsep 5168 | Derive ~ ax6v (a weakened ... |
| axnulALT 5169 | Alternate proof of ~ axnul... |
| axnul 5170 | The Null Set Axiom of ZF s... |
| 0ex 5172 | The Null Set Axiom of ZF s... |
| al0ssb 5173 | The empty set is the uniqu... |
| sseliALT 5174 | Alternate proof of ~ sseli... |
| csbexg 5175 | The existence of proper su... |
| csbex 5176 | The existence of proper su... |
| unisn2 5177 | A version of ~ unisn witho... |
| nalset 5178 | No set contains all sets. ... |
| vnex 5179 | The universal class does n... |
| vprc 5180 | The universal class is not... |
| nvel 5181 | The universal class does n... |
| inex1 5182 | Separation Scheme (Aussond... |
| inex2 5183 | Separation Scheme (Aussond... |
| inex1g 5184 | Closed-form, generalized S... |
| inex2g 5185 | Sufficient condition for a... |
| ssex 5186 | The subset of a set is als... |
| ssexi 5187 | The subset of a set is als... |
| ssexg 5188 | The subset of a set is als... |
| ssexd 5189 | A subclass of a set is a s... |
| prcssprc 5190 | The superclass of a proper... |
| sselpwd 5191 | Elementhood to a power set... |
| difexg 5192 | Existence of a difference.... |
| difexi 5193 | Existence of a difference,... |
| difexd 5194 | Existence of a difference.... |
| zfausab 5195 | Separation Scheme (Aussond... |
| rabexg 5196 | Separation Scheme in terms... |
| rabex 5197 | Separation Scheme in terms... |
| rabexd 5198 | Separation Scheme in terms... |
| rabex2 5199 | Separation Scheme in terms... |
| rab2ex 5200 | A class abstraction based ... |
| elssabg 5201 | Membership in a class abst... |
| intex 5202 | The intersection of a none... |
| intnex 5203 | If a class intersection is... |
| intexab 5204 | The intersection of a none... |
| intexrab 5205 | The intersection of a none... |
| iinexg 5206 | The existence of a class i... |
| intabs 5207 | Absorption of a redundant ... |
| inuni 5208 | The intersection of a unio... |
| elpw2g 5209 | Membership in a power clas... |
| elpw2 5210 | Membership in a power clas... |
| elpwi2 5211 | Membership in a power clas... |
| elpwi2OLD 5212 | Obsolete version of ~ elpw... |
| pwnss 5213 | The power set of a set is ... |
| pwne 5214 | No set equals its power se... |
| difelpw 5215 | A difference is an element... |
| rabelpw 5216 | A restricted class abstrac... |
| class2set 5217 | Construct, from any class ... |
| class2seteq 5218 | Equality theorem based on ... |
| 0elpw 5219 | Every power class contains... |
| pwne0 5220 | A power class is never emp... |
| 0nep0 5221 | The empty set and its powe... |
| 0inp0 5222 | Something cannot be equal ... |
| unidif0 5223 | The removal of the empty s... |
| iin0 5224 | An indexed intersection of... |
| notzfaus 5225 | In the Separation Scheme ~... |
| notzfausOLD 5226 | Obsolete proof of ~ notzfa... |
| intv 5227 | The intersection of the un... |
| axpweq 5228 | Two equivalent ways to exp... |
| zfpow 5230 | Axiom of Power Sets expres... |
| axpow2 5231 | A variant of the Axiom of ... |
| axpow3 5232 | A variant of the Axiom of ... |
| el 5233 | Every set is an element of... |
| dtru 5234 | At least two sets exist (o... |
| dtrucor 5235 | Corollary of ~ dtru . Thi... |
| dtrucor2 5236 | The theorem form of the de... |
| dvdemo1 5237 | Demonstration of a theorem... |
| dvdemo2 5238 | Demonstration of a theorem... |
| nfnid 5239 | A setvar variable is not f... |
| nfcvb 5240 | The "distinctor" expressio... |
| vpwex 5241 | Power set axiom: the power... |
| pwexg 5242 | Power set axiom expressed ... |
| pwexd 5243 | Deduction version of the p... |
| pwex 5244 | Power set axiom expressed ... |
| pwel 5245 | Quantitative version of ~ ... |
| abssexg 5246 | Existence of a class of su... |
| snexALT 5247 | Alternate proof of ~ snex ... |
| p0ex 5248 | The power set of the empty... |
| p0exALT 5249 | Alternate proof of ~ p0ex ... |
| pp0ex 5250 | The power set of the power... |
| ord3ex 5251 | The ordinal number 3 is a ... |
| dtruALT 5252 | Alternate proof of ~ dtru ... |
| axc16b 5253 | This theorem shows that Ax... |
| eunex 5254 | Existential uniqueness imp... |
| eusv1 5255 | Two ways to express single... |
| eusvnf 5256 | Even if ` x ` is free in `... |
| eusvnfb 5257 | Two ways to say that ` A (... |
| eusv2i 5258 | Two ways to express single... |
| eusv2nf 5259 | Two ways to express single... |
| eusv2 5260 | Two ways to express single... |
| reusv1 5261 | Two ways to express single... |
| reusv2lem1 5262 | Lemma for ~ reusv2 . (Con... |
| reusv2lem2 5263 | Lemma for ~ reusv2 . (Con... |
| reusv2lem3 5264 | Lemma for ~ reusv2 . (Con... |
| reusv2lem4 5265 | Lemma for ~ reusv2 . (Con... |
| reusv2lem5 5266 | Lemma for ~ reusv2 . (Con... |
| reusv2 5267 | Two ways to express single... |
| reusv3i 5268 | Two ways of expressing exi... |
| reusv3 5269 | Two ways to express single... |
| eusv4 5270 | Two ways to express single... |
| alxfr 5271 | Transfer universal quantif... |
| ralxfrd 5272 | Transfer universal quantif... |
| rexxfrd 5273 | Transfer universal quantif... |
| ralxfr2d 5274 | Transfer universal quantif... |
| rexxfr2d 5275 | Transfer universal quantif... |
| ralxfrd2 5276 | Transfer universal quantif... |
| rexxfrd2 5277 | Transfer existence from a ... |
| ralxfr 5278 | Transfer universal quantif... |
| ralxfrALT 5279 | Alternate proof of ~ ralxf... |
| rexxfr 5280 | Transfer existence from a ... |
| rabxfrd 5281 | Membership in a restricted... |
| rabxfr 5282 | Membership in a restricted... |
| reuhypd 5283 | A theorem useful for elimi... |
| reuhyp 5284 | A theorem useful for elimi... |
| zfpair 5285 | The Axiom of Pairing of Ze... |
| axprALT 5286 | Alternate proof of ~ axpr ... |
| axprlem1 5287 | Lemma for ~ axpr . There ... |
| axprlem2 5288 | Lemma for ~ axpr . There ... |
| axprlem3 5289 | Lemma for ~ axpr . Elimin... |
| axprlem4 5290 | Lemma for ~ axpr . The fi... |
| axprlem5 5291 | Lemma for ~ axpr . The se... |
| axpr 5292 | Unabbreviated version of t... |
| zfpair2 5294 | Derive the abbreviated ver... |
| snex 5295 | A singleton is a set. The... |
| prex 5296 | The Axiom of Pairing using... |
| sels 5297 | If a class is a set, then ... |
| elALT 5298 | Alternate proof of ~ el , ... |
| dtruALT2 5299 | Alternate proof of ~ dtru ... |
| snelpwi 5300 | A singleton of a set belon... |
| snelpw 5301 | A singleton of a set belon... |
| prelpw 5302 | A pair of two sets belongs... |
| prelpwi 5303 | A pair of two sets belongs... |
| rext 5304 | A theorem similar to exten... |
| sspwb 5305 | The powerclass constructio... |
| unipw 5306 | A class equals the union o... |
| univ 5307 | The union of the universe ... |
| pwtr 5308 | A class is transitive iff ... |
| ssextss 5309 | An extensionality-like pri... |
| ssext 5310 | An extensionality-like pri... |
| nssss 5311 | Negation of subclass relat... |
| pweqb 5312 | Classes are equal if and o... |
| intid 5313 | The intersection of all se... |
| moabex 5314 | "At most one" existence im... |
| rmorabex 5315 | Restricted "at most one" e... |
| euabex 5316 | The abstraction of a wff w... |
| nnullss 5317 | A nonempty class (even if ... |
| exss 5318 | Restricted existence in a ... |
| opex 5319 | An ordered pair of classes... |
| otex 5320 | An ordered triple of class... |
| elopg 5321 | Characterization of the el... |
| elop 5322 | Characterization of the el... |
| opi1 5323 | One of the two elements in... |
| opi2 5324 | One of the two elements of... |
| opeluu 5325 | Each member of an ordered ... |
| op1stb 5326 | Extract the first member o... |
| brv 5327 | Two classes are always in ... |
| opnz 5328 | An ordered pair is nonempt... |
| opnzi 5329 | An ordered pair is nonempt... |
| opth1 5330 | Equality of the first memb... |
| opth 5331 | The ordered pair theorem. ... |
| opthg 5332 | Ordered pair theorem. ` C ... |
| opth1g 5333 | Equality of the first memb... |
| opthg2 5334 | Ordered pair theorem. (Co... |
| opth2 5335 | Ordered pair theorem. (Co... |
| opthneg 5336 | Two ordered pairs are not ... |
| opthne 5337 | Two ordered pairs are not ... |
| otth2 5338 | Ordered triple theorem, wi... |
| otth 5339 | Ordered triple theorem. (... |
| otthg 5340 | Ordered triple theorem, cl... |
| eqvinop 5341 | A variable introduction la... |
| sbcop1 5342 | The proper substitution of... |
| sbcop 5343 | The proper substitution of... |
| copsexgw 5344 | Version of ~ copsexg with ... |
| copsexg 5345 | Substitution of class ` A ... |
| copsex2t 5346 | Closed theorem form of ~ c... |
| copsex2g 5347 | Implicit substitution infe... |
| copsex2gOLD 5348 | Obsolete version of ~ cops... |
| copsex4g 5349 | An implicit substitution i... |
| 0nelop 5350 | A property of ordered pair... |
| opwo0id 5351 | An ordered pair is equal t... |
| opeqex 5352 | Equivalence of existence i... |
| oteqex2 5353 | Equivalence of existence i... |
| oteqex 5354 | Equivalence of existence i... |
| opcom 5355 | An ordered pair commutes i... |
| moop2 5356 | "At most one" property of ... |
| opeqsng 5357 | Equivalence for an ordered... |
| opeqsn 5358 | Equivalence for an ordered... |
| opeqpr 5359 | Equivalence for an ordered... |
| snopeqop 5360 | Equivalence for an ordered... |
| propeqop 5361 | Equivalence for an ordered... |
| propssopi 5362 | If a pair of ordered pairs... |
| snopeqopsnid 5363 | Equivalence for an ordered... |
| mosubopt 5364 | "At most one" remains true... |
| mosubop 5365 | "At most one" remains true... |
| euop2 5366 | Transfer existential uniqu... |
| euotd 5367 | Prove existential uniquene... |
| opthwiener 5368 | Justification theorem for ... |
| uniop 5369 | The union of an ordered pa... |
| uniopel 5370 | Ordered pair membership is... |
| opthhausdorff 5371 | Justification theorem for ... |
| opthhausdorff0 5372 | Justification theorem for ... |
| otsndisj 5373 | The singletons consisting ... |
| otiunsndisj 5374 | The union of singletons co... |
| iunopeqop 5375 | Implication of an ordered ... |
| brsnop 5376 | Binary relation for an ord... |
| opabidw 5377 | The law of concretion. Sp... |
| opabid 5378 | The law of concretion. Sp... |
| elopab 5379 | Membership in a class abst... |
| rexopabb 5380 | Restricted existential qua... |
| vopelopabsb 5381 | The law of concretion in t... |
| opelopabsb 5382 | The law of concretion in t... |
| brabsb 5383 | The law of concretion in t... |
| opelopabt 5384 | Closed theorem form of ~ o... |
| opelopabga 5385 | The law of concretion. Th... |
| brabga 5386 | The law of concretion for ... |
| opelopab2a 5387 | Ordered pair membership in... |
| opelopaba 5388 | The law of concretion. Th... |
| braba 5389 | The law of concretion for ... |
| opelopabg 5390 | The law of concretion. Th... |
| brabg 5391 | The law of concretion for ... |
| opelopabgf 5392 | The law of concretion. Th... |
| opelopab2 5393 | Ordered pair membership in... |
| opelopab 5394 | The law of concretion. Th... |
| brab 5395 | The law of concretion for ... |
| opelopabaf 5396 | The law of concretion. Th... |
| opelopabf 5397 | The law of concretion. Th... |
| ssopab2 5398 | Equivalence of ordered pai... |
| ssopab2bw 5399 | Equivalence of ordered pai... |
| eqopab2bw 5400 | Equivalence of ordered pai... |
| ssopab2b 5401 | Equivalence of ordered pai... |
| ssopab2i 5402 | Inference of ordered pair ... |
| ssopab2dv 5403 | Inference of ordered pair ... |
| eqopab2b 5404 | Equivalence of ordered pai... |
| opabn0 5405 | Nonempty ordered pair clas... |
| opab0 5406 | Empty ordered pair class a... |
| csbopab 5407 | Move substitution into a c... |
| csbopabgALT 5408 | Move substitution into a c... |
| csbmpt12 5409 | Move substitution into a m... |
| csbmpt2 5410 | Move substitution into the... |
| iunopab 5411 | Move indexed union inside ... |
| elopabr 5412 | Membership in an ordered-p... |
| elopabran 5413 | Membership in an ordered-p... |
| rbropapd 5414 | Properties of a pair in an... |
| rbropap 5415 | Properties of a pair in a ... |
| 2rbropap 5416 | Properties of a pair in a ... |
| 0nelopab 5417 | The empty set is never an ... |
| brabv 5418 | If two classes are in a re... |
| pwin 5419 | The power class of the int... |
| pwunssOLD 5420 | Obsolete version of ~ pwun... |
| pwssun 5421 | The power class of the uni... |
| pwundifOLD 5422 | Obsolete proof of ~ pwundi... |
| pwun 5423 | The power class of the uni... |
| dfid4 5426 | The identity function expr... |
| dfid3 5427 | A stronger version of ~ df... |
| dfid2 5428 | Alternate definition of th... |
| epelg 5431 | The membership relation an... |
| epeli 5432 | The membership relation an... |
| epel 5433 | The membership relation an... |
| 0sn0ep 5434 | An example for the members... |
| epn0 5435 | The membership relation is... |
| poss 5440 | Subset theorem for the par... |
| poeq1 5441 | Equality theorem for parti... |
| poeq2 5442 | Equality theorem for parti... |
| nfpo 5443 | Bound-variable hypothesis ... |
| nfso 5444 | Bound-variable hypothesis ... |
| pocl 5445 | Properties of partial orde... |
| ispod 5446 | Sufficient conditions for ... |
| swopolem 5447 | Perform the substitutions ... |
| swopo 5448 | A strict weak order is a p... |
| poirr 5449 | A partial order relation i... |
| potr 5450 | A partial order relation i... |
| po2nr 5451 | A partial order relation h... |
| po3nr 5452 | A partial order relation h... |
| po2ne 5453 | Two classes which are in a... |
| po0 5454 | Any relation is a partial ... |
| pofun 5455 | A function preserves a par... |
| sopo 5456 | A strict linear order is a... |
| soss 5457 | Subset theorem for the str... |
| soeq1 5458 | Equality theorem for the s... |
| soeq2 5459 | Equality theorem for the s... |
| sonr 5460 | A strict order relation is... |
| sotr 5461 | A strict order relation is... |
| solin 5462 | A strict order relation is... |
| so2nr 5463 | A strict order relation ha... |
| so3nr 5464 | A strict order relation ha... |
| sotric 5465 | A strict order relation sa... |
| sotrieq 5466 | Trichotomy law for strict ... |
| sotrieq2 5467 | Trichotomy law for strict ... |
| soasym 5468 | Asymmetry law for strict o... |
| sotr2 5469 | A transitivity relation. ... |
| issod 5470 | An irreflexive, transitive... |
| issoi 5471 | An irreflexive, transitive... |
| isso2i 5472 | Deduce strict ordering fro... |
| so0 5473 | Any relation is a strict o... |
| somo 5474 | A totally ordered set has ... |
| fri 5481 | Property of well-founded r... |
| seex 5482 | The ` R ` -preimage of an ... |
| exse 5483 | Any relation on a set is s... |
| dffr2 5484 | Alternate definition of we... |
| frc 5485 | Property of well-founded r... |
| frss 5486 | Subset theorem for the wel... |
| sess1 5487 | Subset theorem for the set... |
| sess2 5488 | Subset theorem for the set... |
| freq1 5489 | Equality theorem for the w... |
| freq2 5490 | Equality theorem for the w... |
| seeq1 5491 | Equality theorem for the s... |
| seeq2 5492 | Equality theorem for the s... |
| nffr 5493 | Bound-variable hypothesis ... |
| nfse 5494 | Bound-variable hypothesis ... |
| nfwe 5495 | Bound-variable hypothesis ... |
| frirr 5496 | A well-founded relation is... |
| fr2nr 5497 | A well-founded relation ha... |
| fr0 5498 | Any relation is well-found... |
| frminex 5499 | If an element of a well-fo... |
| efrirr 5500 | A well-founded class does ... |
| efrn2lp 5501 | A well-founded class conta... |
| epse 5502 | The membership relation is... |
| tz7.2 5503 | Similar to Theorem 7.2 of ... |
| dfepfr 5504 | An alternate way of saying... |
| epfrc 5505 | A subset of a well-founded... |
| wess 5506 | Subset theorem for the wel... |
| weeq1 5507 | Equality theorem for the w... |
| weeq2 5508 | Equality theorem for the w... |
| wefr 5509 | A well-ordering is well-fo... |
| weso 5510 | A well-ordering is a stric... |
| wecmpep 5511 | The elements of a class we... |
| wetrep 5512 | On a class well-ordered by... |
| wefrc 5513 | A nonempty subclass of a c... |
| we0 5514 | Any relation is a well-ord... |
| wereu 5515 | A subset of a well-ordered... |
| wereu2 5516 | All nonempty subclasses of... |
| xpeq1 5533 | Equality theorem for Carte... |
| xpss12 5534 | Subset theorem for Cartesi... |
| xpss 5535 | A Cartesian product is inc... |
| inxpssres 5536 | Intersection with a Cartes... |
| relxp 5537 | A Cartesian product is a r... |
| xpss1 5538 | Subset relation for Cartes... |
| xpss2 5539 | Subset relation for Cartes... |
| xpeq2 5540 | Equality theorem for Carte... |
| elxpi 5541 | Membership in a Cartesian ... |
| elxp 5542 | Membership in a Cartesian ... |
| elxp2 5543 | Membership in a Cartesian ... |
| xpeq12 5544 | Equality theorem for Carte... |
| xpeq1i 5545 | Equality inference for Car... |
| xpeq2i 5546 | Equality inference for Car... |
| xpeq12i 5547 | Equality inference for Car... |
| xpeq1d 5548 | Equality deduction for Car... |
| xpeq2d 5549 | Equality deduction for Car... |
| xpeq12d 5550 | Equality deduction for Car... |
| sqxpeqd 5551 | Equality deduction for a C... |
| nfxp 5552 | Bound-variable hypothesis ... |
| 0nelxp 5553 | The empty set is not a mem... |
| 0nelelxp 5554 | A member of a Cartesian pr... |
| opelxp 5555 | Ordered pair membership in... |
| opelxpi 5556 | Ordered pair membership in... |
| opelxpd 5557 | Ordered pair membership in... |
| opelvv 5558 | Ordered pair membership in... |
| opelvvg 5559 | Ordered pair membership in... |
| opelxp1 5560 | The first member of an ord... |
| opelxp2 5561 | The second member of an or... |
| otelxp1 5562 | The first member of an ord... |
| otel3xp 5563 | An ordered triple is an el... |
| opabssxpd 5564 | An ordered-pair class abst... |
| rabxp 5565 | Class abstraction restrict... |
| brxp 5566 | Binary relation on a Carte... |
| pwvrel 5567 | A set is a binary relation... |
| pwvabrel 5568 | The powerclass of the cart... |
| brrelex12 5569 | Two classes related by a b... |
| brrelex1 5570 | If two classes are related... |
| brrelex2 5571 | If two classes are related... |
| brrelex12i 5572 | Two classes that are relat... |
| brrelex1i 5573 | The first argument of a bi... |
| brrelex2i 5574 | The second argument of a b... |
| nprrel12 5575 | Proper classes are not rel... |
| nprrel 5576 | No proper class is related... |
| 0nelrel0 5577 | A binary relation does not... |
| 0nelrel 5578 | A binary relation does not... |
| fconstmpt 5579 | Representation of a consta... |
| vtoclr 5580 | Variable to class conversi... |
| opthprc 5581 | Justification theorem for ... |
| brel 5582 | Two things in a binary rel... |
| elxp3 5583 | Membership in a Cartesian ... |
| opeliunxp 5584 | Membership in a union of C... |
| xpundi 5585 | Distributive law for Carte... |
| xpundir 5586 | Distributive law for Carte... |
| xpiundi 5587 | Distributive law for Carte... |
| xpiundir 5588 | Distributive law for Carte... |
| iunxpconst 5589 | Membership in a union of C... |
| xpun 5590 | The Cartesian product of t... |
| elvv 5591 | Membership in universal cl... |
| elvvv 5592 | Membership in universal cl... |
| elvvuni 5593 | An ordered pair contains i... |
| brinxp2 5594 | Intersection of binary rel... |
| brinxp 5595 | Intersection of binary rel... |
| opelinxp 5596 | Ordered pair element in an... |
| poinxp 5597 | Intersection of partial or... |
| soinxp 5598 | Intersection of total orde... |
| frinxp 5599 | Intersection of well-found... |
| seinxp 5600 | Intersection of set-like r... |
| weinxp 5601 | Intersection of well-order... |
| posn 5602 | Partial ordering of a sing... |
| sosn 5603 | Strict ordering on a singl... |
| frsn 5604 | Founded relation on a sing... |
| wesn 5605 | Well-ordering of a singlet... |
| elopaelxp 5606 | Membership in an ordered-p... |
| bropaex12 5607 | Two classes related by an ... |
| opabssxp 5608 | An abstraction relation is... |
| brab2a 5609 | The law of concretion for ... |
| optocl 5610 | Implicit substitution of c... |
| 2optocl 5611 | Implicit substitution of c... |
| 3optocl 5612 | Implicit substitution of c... |
| opbrop 5613 | Ordered pair membership in... |
| 0xp 5614 | The Cartesian product with... |
| csbxp 5615 | Distribute proper substitu... |
| releq 5616 | Equality theorem for the r... |
| releqi 5617 | Equality inference for the... |
| releqd 5618 | Equality deduction for the... |
| nfrel 5619 | Bound-variable hypothesis ... |
| sbcrel 5620 | Distribute proper substitu... |
| relss 5621 | Subclass theorem for relat... |
| ssrel 5622 | A subclass relationship de... |
| eqrel 5623 | Extensionality principle f... |
| ssrel2 5624 | A subclass relationship de... |
| relssi 5625 | Inference from subclass pr... |
| relssdv 5626 | Deduction from subclass pr... |
| eqrelriv 5627 | Inference from extensional... |
| eqrelriiv 5628 | Inference from extensional... |
| eqbrriv 5629 | Inference from extensional... |
| eqrelrdv 5630 | Deduce equality of relatio... |
| eqbrrdv 5631 | Deduction from extensional... |
| eqbrrdiv 5632 | Deduction from extensional... |
| eqrelrdv2 5633 | A version of ~ eqrelrdv . ... |
| ssrelrel 5634 | A subclass relationship de... |
| eqrelrel 5635 | Extensionality principle f... |
| elrel 5636 | A member of a relation is ... |
| rel0 5637 | The empty set is a relatio... |
| nrelv 5638 | The universal class is not... |
| relsng 5639 | A singleton is a relation ... |
| relsnb 5640 | An at-most-singleton is a ... |
| relsnopg 5641 | A singleton of an ordered ... |
| relsn 5642 | A singleton is a relation ... |
| relsnop 5643 | A singleton of an ordered ... |
| copsex2gb 5644 | Implicit substitution infe... |
| copsex2ga 5645 | Implicit substitution infe... |
| elopaba 5646 | Membership in an ordered-p... |
| xpsspw 5647 | A Cartesian product is inc... |
| unixpss 5648 | The double class union of ... |
| relun 5649 | The union of two relations... |
| relin1 5650 | The intersection with a re... |
| relin2 5651 | The intersection with a re... |
| relinxp 5652 | Intersection with a Cartes... |
| reldif 5653 | A difference cutting down ... |
| reliun 5654 | An indexed union is a rela... |
| reliin 5655 | An indexed intersection is... |
| reluni 5656 | The union of a class is a ... |
| relint 5657 | The intersection of a clas... |
| relopabiv 5658 | A class of ordered pairs i... |
| relopabv 5659 | A class of ordered pairs i... |
| relopabi 5660 | A class of ordered pairs i... |
| relopabiALT 5661 | Alternate proof of ~ relop... |
| relopab 5662 | A class of ordered pairs i... |
| mptrel 5663 | The maps-to notation alway... |
| reli 5664 | The identity relation is a... |
| rele 5665 | The membership relation is... |
| opabid2 5666 | A relation expressed as an... |
| inopab 5667 | Intersection of two ordere... |
| difopab 5668 | Difference of two ordered-... |
| inxp 5669 | Intersection of two Cartes... |
| xpindi 5670 | Distributive law for Carte... |
| xpindir 5671 | Distributive law for Carte... |
| xpiindi 5672 | Distributive law for Carte... |
| xpriindi 5673 | Distributive law for Carte... |
| eliunxp 5674 | Membership in a union of C... |
| opeliunxp2 5675 | Membership in a union of C... |
| raliunxp 5676 | Write a double restricted ... |
| rexiunxp 5677 | Write a double restricted ... |
| ralxp 5678 | Universal quantification r... |
| rexxp 5679 | Existential quantification... |
| exopxfr 5680 | Transfer ordered-pair exis... |
| exopxfr2 5681 | Transfer ordered-pair exis... |
| djussxp 5682 | Disjoint union is a subset... |
| ralxpf 5683 | Version of ~ ralxp with bo... |
| rexxpf 5684 | Version of ~ rexxp with bo... |
| iunxpf 5685 | Indexed union on a Cartesi... |
| opabbi2dv 5686 | Deduce equality of a relat... |
| relop 5687 | A necessary and sufficient... |
| ideqg 5688 | For sets, the identity rel... |
| ideq 5689 | For sets, the identity rel... |
| ididg 5690 | A set is identical to itse... |
| issetid 5691 | Two ways of expressing set... |
| coss1 5692 | Subclass theorem for compo... |
| coss2 5693 | Subclass theorem for compo... |
| coeq1 5694 | Equality theorem for compo... |
| coeq2 5695 | Equality theorem for compo... |
| coeq1i 5696 | Equality inference for com... |
| coeq2i 5697 | Equality inference for com... |
| coeq1d 5698 | Equality deduction for com... |
| coeq2d 5699 | Equality deduction for com... |
| coeq12i 5700 | Equality inference for com... |
| coeq12d 5701 | Equality deduction for com... |
| nfco 5702 | Bound-variable hypothesis ... |
| brcog 5703 | Ordered pair membership in... |
| opelco2g 5704 | Ordered pair membership in... |
| brcogw 5705 | Ordered pair membership in... |
| eqbrrdva 5706 | Deduction from extensional... |
| brco 5707 | Binary relation on a compo... |
| opelco 5708 | Ordered pair membership in... |
| cnvss 5709 | Subset theorem for convers... |
| cnveq 5710 | Equality theorem for conve... |
| cnveqi 5711 | Equality inference for con... |
| cnveqd 5712 | Equality deduction for con... |
| elcnv 5713 | Membership in a converse r... |
| elcnv2 5714 | Membership in a converse r... |
| nfcnv 5715 | Bound-variable hypothesis ... |
| brcnvg 5716 | The converse of a binary r... |
| opelcnvg 5717 | Ordered-pair membership in... |
| opelcnv 5718 | Ordered-pair membership in... |
| brcnv 5719 | The converse of a binary r... |
| csbcnv 5720 | Move class substitution in... |
| csbcnvgALT 5721 | Move class substitution in... |
| cnvco 5722 | Distributive law of conver... |
| cnvuni 5723 | The converse of a class un... |
| dfdm3 5724 | Alternate definition of do... |
| dfrn2 5725 | Alternate definition of ra... |
| dfrn3 5726 | Alternate definition of ra... |
| elrn2g 5727 | Membership in a range. (C... |
| elrng 5728 | Membership in a range. (C... |
| elrn2 5729 | Membership in a range. (C... |
| elrn 5730 | Membership in a range. (C... |
| ssrelrn 5731 | If a relation is a subset ... |
| dfdm4 5732 | Alternate definition of do... |
| dfdmf 5733 | Definition of domain, usin... |
| csbdm 5734 | Distribute proper substitu... |
| eldmg 5735 | Domain membership. Theore... |
| eldm2g 5736 | Domain membership. Theore... |
| eldm 5737 | Membership in a domain. T... |
| eldm2 5738 | Membership in a domain. T... |
| dmss 5739 | Subset theorem for domain.... |
| dmeq 5740 | Equality theorem for domai... |
| dmeqi 5741 | Equality inference for dom... |
| dmeqd 5742 | Equality deduction for dom... |
| opeldmd 5743 | Membership of first of an ... |
| opeldm 5744 | Membership of first of an ... |
| breldm 5745 | Membership of first of a b... |
| breldmg 5746 | Membership of first of a b... |
| dmun 5747 | The domain of a union is t... |
| dmin 5748 | The domain of an intersect... |
| breldmd 5749 | Membership of first of a b... |
| dmiun 5750 | The domain of an indexed u... |
| dmuni 5751 | The domain of a union. Pa... |
| dmopab 5752 | The domain of a class of o... |
| dmopabelb 5753 | A set is an element of the... |
| dmopab2rex 5754 | The domain of an ordered p... |
| dmopabss 5755 | Upper bound for the domain... |
| dmopab3 5756 | The domain of a restricted... |
| dm0 5757 | The domain of the empty se... |
| dmi 5758 | The domain of the identity... |
| dmv 5759 | The domain of the universe... |
| dmep 5760 | The domain of the membersh... |
| domepOLD 5761 | Obsolete proof of ~ dmep a... |
| dm0rn0 5762 | An empty domain is equival... |
| rn0 5763 | The range of the empty set... |
| rnep 5764 | The range of the membershi... |
| reldm0 5765 | A relation is empty iff it... |
| dmxp 5766 | The domain of a Cartesian ... |
| dmxpid 5767 | The domain of a Cartesian ... |
| dmxpin 5768 | The domain of the intersec... |
| xpid11 5769 | The Cartesian square is a ... |
| dmcnvcnv 5770 | The domain of the double c... |
| rncnvcnv 5771 | The range of the double co... |
| elreldm 5772 | The first member of an ord... |
| rneq 5773 | Equality theorem for range... |
| rneqi 5774 | Equality inference for ran... |
| rneqd 5775 | Equality deduction for ran... |
| rnss 5776 | Subset theorem for range. ... |
| rnssi 5777 | Subclass inference for ran... |
| brelrng 5778 | The second argument of a b... |
| brelrn 5779 | The second argument of a b... |
| opelrn 5780 | Membership of second membe... |
| releldm 5781 | The first argument of a bi... |
| relelrn 5782 | The second argument of a b... |
| releldmb 5783 | Membership in a domain. (... |
| relelrnb 5784 | Membership in a range. (C... |
| releldmi 5785 | The first argument of a bi... |
| relelrni 5786 | The second argument of a b... |
| dfrnf 5787 | Definition of range, using... |
| nfdm 5788 | Bound-variable hypothesis ... |
| nfrn 5789 | Bound-variable hypothesis ... |
| dmiin 5790 | Domain of an intersection.... |
| rnopab 5791 | The range of a class of or... |
| rnmpt 5792 | The range of a function in... |
| elrnmpt 5793 | The range of a function in... |
| elrnmpt1s 5794 | Elementhood in an image se... |
| elrnmpt1 5795 | Elementhood in an image se... |
| elrnmptg 5796 | Membership in the range of... |
| elrnmpti 5797 | Membership in the range of... |
| elrnmptd 5798 | The range of a function in... |
| elrnmptdv 5799 | Elementhood in the range o... |
| elrnmpt2d 5800 | Elementhood in the range o... |
| dfiun3g 5801 | Alternate definition of in... |
| dfiin3g 5802 | Alternate definition of in... |
| dfiun3 5803 | Alternate definition of in... |
| dfiin3 5804 | Alternate definition of in... |
| riinint 5805 | Express a relative indexed... |
| relrn0 5806 | A relation is empty iff it... |
| dmrnssfld 5807 | The domain and range of a ... |
| dmcoss 5808 | Domain of a composition. ... |
| rncoss 5809 | Range of a composition. (... |
| dmcosseq 5810 | Domain of a composition. ... |
| dmcoeq 5811 | Domain of a composition. ... |
| rncoeq 5812 | Range of a composition. (... |
| reseq1 5813 | Equality theorem for restr... |
| reseq2 5814 | Equality theorem for restr... |
| reseq1i 5815 | Equality inference for res... |
| reseq2i 5816 | Equality inference for res... |
| reseq12i 5817 | Equality inference for res... |
| reseq1d 5818 | Equality deduction for res... |
| reseq2d 5819 | Equality deduction for res... |
| reseq12d 5820 | Equality deduction for res... |
| nfres 5821 | Bound-variable hypothesis ... |
| csbres 5822 | Distribute proper substitu... |
| res0 5823 | A restriction to the empty... |
| dfres3 5824 | Alternate definition of re... |
| opelres 5825 | Ordered pair elementhood i... |
| brres 5826 | Binary relation on a restr... |
| opelresi 5827 | Ordered pair membership in... |
| brresi 5828 | Binary relation on a restr... |
| opres 5829 | Ordered pair membership in... |
| resieq 5830 | A restricted identity rela... |
| opelidres 5831 | ` <. A , A >. ` belongs to... |
| resres 5832 | The restriction of a restr... |
| resundi 5833 | Distributive law for restr... |
| resundir 5834 | Distributive law for restr... |
| resindi 5835 | Class restriction distribu... |
| resindir 5836 | Class restriction distribu... |
| inres 5837 | Move intersection into cla... |
| resdifcom 5838 | Commutative law for restri... |
| resiun1 5839 | Distribution of restrictio... |
| resiun2 5840 | Distribution of restrictio... |
| dmres 5841 | The domain of a restrictio... |
| ssdmres 5842 | A domain restricted to a s... |
| dmresexg 5843 | The domain of a restrictio... |
| resss 5844 | A class includes its restr... |
| rescom 5845 | Commutative law for restri... |
| ssres 5846 | Subclass theorem for restr... |
| ssres2 5847 | Subclass theorem for restr... |
| relres 5848 | A restriction is a relatio... |
| resabs1 5849 | Absorption law for restric... |
| resabs1d 5850 | Absorption law for restric... |
| resabs2 5851 | Absorption law for restric... |
| residm 5852 | Idempotent law for restric... |
| resima 5853 | A restriction to an image.... |
| resima2 5854 | Image under a restricted c... |
| rnresss 5855 | The range of a restriction... |
| xpssres 5856 | Restriction of a constant ... |
| elinxp 5857 | Membership in an intersect... |
| elres 5858 | Membership in a restrictio... |
| elsnres 5859 | Membership in restriction ... |
| relssres 5860 | Simplification law for res... |
| dmressnsn 5861 | The domain of a restrictio... |
| eldmressnsn 5862 | The element of the domain ... |
| eldmeldmressn 5863 | An element of the domain (... |
| resdm 5864 | A relation restricted to i... |
| resexg 5865 | The restriction of a set i... |
| resexd 5866 | The restriction of a set i... |
| resex 5867 | The restriction of a set i... |
| resindm 5868 | When restricting a relatio... |
| resdmdfsn 5869 | Restricting a relation to ... |
| resopab 5870 | Restriction of a class abs... |
| iss 5871 | A subclass of the identity... |
| resopab2 5872 | Restriction of a class abs... |
| resmpt 5873 | Restriction of the mapping... |
| resmpt3 5874 | Unconditional restriction ... |
| resmptf 5875 | Restriction of the mapping... |
| resmptd 5876 | Restriction of the mapping... |
| dfres2 5877 | Alternate definition of th... |
| mptss 5878 | Sufficient condition for i... |
| elidinxp 5879 | Characterization of the el... |
| elidinxpid 5880 | Characterization of the el... |
| elrid 5881 | Characterization of the el... |
| idinxpres 5882 | The intersection of the id... |
| idinxpresid 5883 | The intersection of the id... |
| idssxp 5884 | A diagonal set as a subset... |
| opabresid 5885 | The restricted identity re... |
| mptresid 5886 | The restricted identity re... |
| opabresidOLD 5887 | Obsolete version of ~ opab... |
| mptresidOLD 5888 | Obsolete version of ~ mptr... |
| dmresi 5889 | The domain of a restricted... |
| restidsing 5890 | Restriction of the identit... |
| iresn0n0 5891 | The identity function rest... |
| imaeq1 5892 | Equality theorem for image... |
| imaeq2 5893 | Equality theorem for image... |
| imaeq1i 5894 | Equality theorem for image... |
| imaeq2i 5895 | Equality theorem for image... |
| imaeq1d 5896 | Equality theorem for image... |
| imaeq2d 5897 | Equality theorem for image... |
| imaeq12d 5898 | Equality theorem for image... |
| dfima2 5899 | Alternate definition of im... |
| dfima3 5900 | Alternate definition of im... |
| elimag 5901 | Membership in an image. T... |
| elima 5902 | Membership in an image. T... |
| elima2 5903 | Membership in an image. T... |
| elima3 5904 | Membership in an image. T... |
| nfima 5905 | Bound-variable hypothesis ... |
| nfimad 5906 | Deduction version of bound... |
| imadmrn 5907 | The image of the domain of... |
| imassrn 5908 | The image of a class is a ... |
| mptima 5909 | Image of a function in map... |
| imai 5910 | Image under the identity r... |
| rnresi 5911 | The range of the restricte... |
| resiima 5912 | The image of a restriction... |
| ima0 5913 | Image of the empty set. T... |
| 0ima 5914 | Image under the empty rela... |
| csbima12 5915 | Move class substitution in... |
| imadisj 5916 | A class whose image under ... |
| cnvimass 5917 | A preimage under any class... |
| cnvimarndm 5918 | The preimage of the range ... |
| imasng 5919 | The image of a singleton. ... |
| relimasn 5920 | The image of a singleton. ... |
| elrelimasn 5921 | Elementhood in the image o... |
| elimasn 5922 | Membership in an image of ... |
| elimasng 5923 | Membership in an image of ... |
| elimasni 5924 | Membership in an image of ... |
| args 5925 | Two ways to express the cl... |
| eliniseg 5926 | Membership in an initial s... |
| epini 5927 | Any set is equal to its pr... |
| iniseg 5928 | An idiom that signifies an... |
| inisegn0 5929 | Nonemptiness of an initial... |
| dffr3 5930 | Alternate definition of we... |
| dfse2 5931 | Alternate definition of se... |
| imass1 5932 | Subset theorem for image. ... |
| imass2 5933 | Subset theorem for image. ... |
| ndmima 5934 | The image of a singleton o... |
| relcnv 5935 | A converse is a relation. ... |
| relbrcnvg 5936 | When ` R ` is a relation, ... |
| eliniseg2 5937 | Eliminate the class existe... |
| relbrcnv 5938 | When ` R ` is a relation, ... |
| cotrg 5939 | Two ways of saying that th... |
| cotr 5940 | Two ways of saying a relat... |
| idrefALT 5941 | Alternate proof of ~ idref... |
| cnvsym 5942 | Two ways of saying a relat... |
| intasym 5943 | Two ways of saying a relat... |
| asymref 5944 | Two ways of saying a relat... |
| asymref2 5945 | Two ways of saying a relat... |
| intirr 5946 | Two ways of saying a relat... |
| brcodir 5947 | Two ways of saying that tw... |
| codir 5948 | Two ways of saying a relat... |
| qfto 5949 | A quantifier-free way of e... |
| xpidtr 5950 | A Cartesian square is a tr... |
| trin2 5951 | The intersection of two tr... |
| poirr2 5952 | A partial order relation i... |
| trinxp 5953 | The relation induced by a ... |
| soirri 5954 | A strict order relation is... |
| sotri 5955 | A strict order relation is... |
| son2lpi 5956 | A strict order relation ha... |
| sotri2 5957 | A transitivity relation. ... |
| sotri3 5958 | A transitivity relation. ... |
| poleloe 5959 | Express "less than or equa... |
| poltletr 5960 | Transitive law for general... |
| somin1 5961 | Property of a minimum in a... |
| somincom 5962 | Commutativity of minimum i... |
| somin2 5963 | Property of a minimum in a... |
| soltmin 5964 | Being less than a minimum,... |
| cnvopab 5965 | The converse of a class ab... |
| mptcnv 5966 | The converse of a mapping ... |
| cnv0 5967 | The converse of the empty ... |
| cnvi 5968 | The converse of the identi... |
| cnvun 5969 | The converse of a union is... |
| cnvdif 5970 | Distributive law for conve... |
| cnvin 5971 | Distributive law for conve... |
| rnun 5972 | Distributive law for range... |
| rnin 5973 | The range of an intersecti... |
| rniun 5974 | The range of an indexed un... |
| rnuni 5975 | The range of a union. Par... |
| imaundi 5976 | Distributive law for image... |
| imaundir 5977 | The image of a union. (Co... |
| cnvimassrndm 5978 | The preimage of a superset... |
| dminss 5979 | An upper bound for interse... |
| imainss 5980 | An upper bound for interse... |
| inimass 5981 | The image of an intersecti... |
| inimasn 5982 | The intersection of the im... |
| cnvxp 5983 | The converse of a Cartesia... |
| xp0 5984 | The Cartesian product with... |
| xpnz 5985 | The Cartesian product of n... |
| xpeq0 5986 | At least one member of an ... |
| xpdisj1 5987 | Cartesian products with di... |
| xpdisj2 5988 | Cartesian products with di... |
| xpsndisj 5989 | Cartesian products with tw... |
| difxp 5990 | Difference of Cartesian pr... |
| difxp1 5991 | Difference law for Cartesi... |
| difxp2 5992 | Difference law for Cartesi... |
| djudisj 5993 | Disjoint unions with disjo... |
| xpdifid 5994 | The set of distinct couple... |
| resdisj 5995 | A double restriction to di... |
| rnxp 5996 | The range of a Cartesian p... |
| dmxpss 5997 | The domain of a Cartesian ... |
| rnxpss 5998 | The range of a Cartesian p... |
| rnxpid 5999 | The range of a Cartesian s... |
| ssxpb 6000 | A Cartesian product subcla... |
| xp11 6001 | The Cartesian product of n... |
| xpcan 6002 | Cancellation law for Carte... |
| xpcan2 6003 | Cancellation law for Carte... |
| ssrnres 6004 | Two ways to express surjec... |
| rninxp 6005 | Two ways to express surjec... |
| dminxp 6006 | Two ways to express totali... |
| imainrect 6007 | Image by a restricted and ... |
| xpima 6008 | Direct image by a Cartesia... |
| xpima1 6009 | Direct image by a Cartesia... |
| xpima2 6010 | Direct image by a Cartesia... |
| xpimasn 6011 | Direct image of a singleto... |
| sossfld 6012 | The base set of a strict o... |
| sofld 6013 | The base set of a nonempty... |
| cnvcnv3 6014 | The set of all ordered pai... |
| dfrel2 6015 | Alternate definition of re... |
| dfrel4v 6016 | A relation can be expresse... |
| dfrel4 6017 | A relation can be expresse... |
| cnvcnv 6018 | The double converse of a c... |
| cnvcnv2 6019 | The double converse of a c... |
| cnvcnvss 6020 | The double converse of a c... |
| cnvrescnv 6021 | Two ways to express the co... |
| cnveqb 6022 | Equality theorem for conve... |
| cnveq0 6023 | A relation empty iff its c... |
| dfrel3 6024 | Alternate definition of re... |
| elid 6025 | Characterization of the el... |
| dmresv 6026 | The domain of a universal ... |
| rnresv 6027 | The range of a universal r... |
| dfrn4 6028 | Range defined in terms of ... |
| csbrn 6029 | Distribute proper substitu... |
| rescnvcnv 6030 | The restriction of the dou... |
| cnvcnvres 6031 | The double converse of the... |
| imacnvcnv 6032 | The image of the double co... |
| dmsnn0 6033 | The domain of a singleton ... |
| rnsnn0 6034 | The range of a singleton i... |
| dmsn0 6035 | The domain of the singleto... |
| cnvsn0 6036 | The converse of the single... |
| dmsn0el 6037 | The domain of a singleton ... |
| relsn2 6038 | A singleton is a relation ... |
| dmsnopg 6039 | The domain of a singleton ... |
| dmsnopss 6040 | The domain of a singleton ... |
| dmpropg 6041 | The domain of an unordered... |
| dmsnop 6042 | The domain of a singleton ... |
| dmprop 6043 | The domain of an unordered... |
| dmtpop 6044 | The domain of an unordered... |
| cnvcnvsn 6045 | Double converse of a singl... |
| dmsnsnsn 6046 | The domain of the singleto... |
| rnsnopg 6047 | The range of a singleton o... |
| rnpropg 6048 | The range of a pair of ord... |
| cnvsng 6049 | Converse of a singleton of... |
| rnsnop 6050 | The range of a singleton o... |
| op1sta 6051 | Extract the first member o... |
| cnvsn 6052 | Converse of a singleton of... |
| op2ndb 6053 | Extract the second member ... |
| op2nda 6054 | Extract the second member ... |
| opswap 6055 | Swap the members of an ord... |
| cnvresima 6056 | An image under the convers... |
| resdm2 6057 | A class restricted to its ... |
| resdmres 6058 | Restriction to the domain ... |
| resresdm 6059 | A restriction by an arbitr... |
| imadmres 6060 | The image of the domain of... |
| resdmss 6061 | Subset relationship for th... |
| resdifdi 6062 | Distributive law for restr... |
| resdifdir 6063 | Distributive law for restr... |
| mptpreima 6064 | The preimage of a function... |
| mptiniseg 6065 | Converse singleton image o... |
| dmmpt 6066 | The domain of the mapping ... |
| dmmptss 6067 | The domain of a mapping is... |
| dmmptg 6068 | The domain of the mapping ... |
| rnmpt0f 6069 | The range of a function in... |
| rnmptn0 6070 | The range of a function in... |
| relco 6071 | A composition is a relatio... |
| dfco2 6072 | Alternate definition of a ... |
| dfco2a 6073 | Generalization of ~ dfco2 ... |
| coundi 6074 | Class composition distribu... |
| coundir 6075 | Class composition distribu... |
| cores 6076 | Restricted first member of... |
| resco 6077 | Associative law for the re... |
| imaco 6078 | Image of the composition o... |
| rnco 6079 | The range of the compositi... |
| rnco2 6080 | The range of the compositi... |
| dmco 6081 | The domain of a compositio... |
| coeq0 6082 | A composition of two relat... |
| coiun 6083 | Composition with an indexe... |
| cocnvcnv1 6084 | A composition is not affec... |
| cocnvcnv2 6085 | A composition is not affec... |
| cores2 6086 | Absorption of a reverse (p... |
| co02 6087 | Composition with the empty... |
| co01 6088 | Composition with the empty... |
| coi1 6089 | Composition with the ident... |
| coi2 6090 | Composition with the ident... |
| coires1 6091 | Composition with a restric... |
| coass 6092 | Associative law for class ... |
| relcnvtrg 6093 | General form of ~ relcnvtr... |
| relcnvtr 6094 | A relation is transitive i... |
| relssdmrn 6095 | A relation is included in ... |
| resssxp 6096 | If the ` R ` -image of a c... |
| cnvssrndm 6097 | The converse is a subset o... |
| cossxp 6098 | Composition as a subset of... |
| relrelss 6099 | Two ways to describe the s... |
| unielrel 6100 | The membership relation fo... |
| relfld 6101 | The double union of a rela... |
| relresfld 6102 | Restriction of a relation ... |
| relcoi2 6103 | Composition with the ident... |
| relcoi1 6104 | Composition with the ident... |
| unidmrn 6105 | The double union of the co... |
| relcnvfld 6106 | if ` R ` is a relation, it... |
| dfdm2 6107 | Alternate definition of do... |
| unixp 6108 | The double class union of ... |
| unixp0 6109 | A Cartesian product is emp... |
| unixpid 6110 | Field of a Cartesian squar... |
| ressn 6111 | Restriction of a class to ... |
| cnviin 6112 | The converse of an interse... |
| cnvpo 6113 | The converse of a partial ... |
| cnvso 6114 | The converse of a strict o... |
| xpco 6115 | Composition of two Cartesi... |
| xpcoid 6116 | Composition of two Cartesi... |
| elsnxp 6117 | Membership in a Cartesian ... |
| reu3op 6118 | There is a unique ordered ... |
| reuop 6119 | There is a unique ordered ... |
| opreu2reurex 6120 | There is a unique ordered ... |
| opreu2reu 6121 | If there is a unique order... |
| predeq123 6124 | Equality theorem for the p... |
| predeq1 6125 | Equality theorem for the p... |
| predeq2 6126 | Equality theorem for the p... |
| predeq3 6127 | Equality theorem for the p... |
| nfpred 6128 | Bound-variable hypothesis ... |
| predpredss 6129 | If ` A ` is a subset of ` ... |
| predss 6130 | The predecessor class of `... |
| sspred 6131 | Another subset/predecessor... |
| dfpred2 6132 | An alternate definition of... |
| dfpred3 6133 | An alternate definition of... |
| dfpred3g 6134 | An alternate definition of... |
| elpredim 6135 | Membership in a predecesso... |
| elpred 6136 | Membership in a predecesso... |
| elpredg 6137 | Membership in a predecesso... |
| predasetex 6138 | The predecessor class exis... |
| dffr4 6139 | Alternate definition of we... |
| predel 6140 | Membership in the predeces... |
| predpo 6141 | Property of the precessor ... |
| predso 6142 | Property of the predecesso... |
| predbrg 6143 | Closed form of ~ elpredim ... |
| setlikespec 6144 | If ` R ` is set-like in ` ... |
| predidm 6145 | Idempotent law for the pre... |
| predin 6146 | Intersection law for prede... |
| predun 6147 | Union law for predecessor ... |
| preddif 6148 | Difference law for predece... |
| predep 6149 | The predecessor under the ... |
| preddowncl 6150 | A property of classes that... |
| predpoirr 6151 | Given a partial ordering, ... |
| predfrirr 6152 | Given a well-founded relat... |
| pred0 6153 | The predecessor class over... |
| tz6.26 6154 | All nonempty subclasses of... |
| tz6.26i 6155 | All nonempty subclasses of... |
| wfi 6156 | The Principle of Well-Foun... |
| wfii 6157 | The Principle of Well-Foun... |
| wfisg 6158 | Well-Founded Induction Sch... |
| wfis 6159 | Well-Founded Induction Sch... |
| wfis2fg 6160 | Well-Founded Induction Sch... |
| wfis2f 6161 | Well Founded Induction sch... |
| wfis2g 6162 | Well-Founded Induction Sch... |
| wfis2 6163 | Well Founded Induction sch... |
| wfis3 6164 | Well Founded Induction sch... |
| ordeq 6173 | Equality theorem for the o... |
| elong 6174 | An ordinal number is an or... |
| elon 6175 | An ordinal number is an or... |
| eloni 6176 | An ordinal number has the ... |
| elon2 6177 | An ordinal number is an or... |
| limeq 6178 | Equality theorem for the l... |
| ordwe 6179 | Membership well-orders eve... |
| ordtr 6180 | An ordinal class is transi... |
| ordfr 6181 | Membership is well-founded... |
| ordelss 6182 | An element of an ordinal c... |
| trssord 6183 | A transitive subclass of a... |
| ordirr 6184 | No ordinal class is a memb... |
| nordeq 6185 | A member of an ordinal cla... |
| ordn2lp 6186 | An ordinal class cannot be... |
| tz7.5 6187 | A nonempty subclass of an ... |
| ordelord 6188 | An element of an ordinal c... |
| tron 6189 | The class of all ordinal n... |
| ordelon 6190 | An element of an ordinal c... |
| onelon 6191 | An element of an ordinal n... |
| tz7.7 6192 | A transitive class belongs... |
| ordelssne 6193 | For ordinal classes, membe... |
| ordelpss 6194 | For ordinal classes, membe... |
| ordsseleq 6195 | For ordinal classes, inclu... |
| ordin 6196 | The intersection of two or... |
| onin 6197 | The intersection of two or... |
| ordtri3or 6198 | A trichotomy law for ordin... |
| ordtri1 6199 | A trichotomy law for ordin... |
| ontri1 6200 | A trichotomy law for ordin... |
| ordtri2 6201 | A trichotomy law for ordin... |
| ordtri3 6202 | A trichotomy law for ordin... |
| ordtri4 6203 | A trichotomy law for ordin... |
| orddisj 6204 | An ordinal class and its s... |
| onfr 6205 | The ordinal class is well-... |
| onelpss |