Bibliographic Cross-References
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Intuitionistic Logic Explorer Bibliographic Cross-References |
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| Bibliographic Reference | Description | Intuitionistic Logic Explorer Page(s) |
|---|---|---|
| [AczelRathjen], p. 71 | Definition 8.1.4 | enumct 7461 fidcenum 7280 |
| [AczelRathjen], p. 72 | Proposition 8.1.11 | fidcenum 7280 |
| [AczelRathjen], p. 73 | Lemma 8.1.14 | enumct 7461 |
| [AczelRathjen], p. 73 | Corollary 8.1.13 | ennnfone 13373 |
| [AczelRathjen], p. 74 | Lemma 8.1.16 | xpfi 7245 |
| [AczelRathjen], p. 74 | Remark 8.1.17 | unfiexmid 7231 |
| [AczelRathjen], p. 74 | Theorem 8.1.19 | ctiunct 13388 |
| [AczelRathjen], p. 75 | Corollary 8.1.20 | unct 13390 |
| [AczelRathjen], p. 75 | Corollary 8.1.23 | qnnen 13379 znnen 13346 |
| [AczelRathjen], p. 77 | Lemma 8.1.27 | omctfn 13391 |
| [AczelRathjen], p. 78 | Theorem 8.1.28 | omiunct 13392 |
| [AczelRathjen], p. 80 | Corollary 8.2.4 | df-ihash 11236 |
| [AczelRathjen], p. 183 | Chapter 20 | ax-setind 4686 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 11380 df-pfx 11466 df-substr 11439 df-word 11326 lencl 11329 wrd0 11350 |
| [Apostol] p. 18 | Theorem I.1 | addcan 8513 addcan2d 8518 addcan2i 8516 addcand 8517 addcani 8515 |
| [Apostol] p. 18 | Theorem I.2 | negeu 8524 |
| [Apostol] p. 18 | Theorem I.3 | negsub 8581 negsubd 8650 negsubi 8611 |
| [Apostol] p. 18 | Theorem I.4 | negneg 8583 negnegd 8635 negnegi 8603 |
| [Apostol] p. 18 | Theorem I.5 | subdi 8719 subdid 8748 subdii 8741 subdir 8720 subdird 8749 subdiri 8742 |
| [Apostol] p. 18 | Theorem I.6 | mul01 8723 mul01d 8727 mul01i 8725 mul02 8721 mul02d 8726 mul02i 8724 |
| [Apostol] p. 18 | Theorem I.9 | divrecapd 9131 |
| [Apostol] p. 18 | Theorem I.10 | recrecapi 9082 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 8732 mul2negd 8747 mul2negi 8740 mulneg1 8729 mulneg1d 8745 mulneg1i 8738 |
| [Apostol] p. 18 | Theorem I.14 | rdivmuldivd 14559 |
| [Apostol] p. 18 | Theorem I.15 | divdivdivap 9051 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 10094 rpaddcld 10129 rpmulcl 10095 rpmulcld 10130 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 10106 |
| [Apostol] p. 20 | Theorem I.17 | lttri 8437 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 8873 ltadd1dd 8891 ltadd1i 8837 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 8928 ltmul1a 8927 ltmul1i 9258 ltmul1ii 9266 ltmul2 9194 ltmul2d 10156 ltmul2dd 10170 ltmul2i 9261 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 8460 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 8803 lt0neg1d 8850 ltneg 8797 ltnegd 8858 ltnegi 8828 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 8780 lt2addd 8903 lt2addi 8845 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 10071 |
| [Apostol] p. 21 | Exercise 4 | recgt0 9188 recgt0d 9272 recgt0i 9244 recgt0ii 9245 |
| [Apostol] p. 22 | Definition of integers | df-z 9654 |
| [Apostol] p. 22 | Definition of rationals | df-q 10035 |
| [Apostol] p. 24 | Theorem I.26 | supeuti 7340 |
| [Apostol] p. 26 | Theorem I.29 | arch 9571 |
| [Apostol] p. 28 | Exercise 2 | btwnz 9775 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 9572 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 10707 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 12662 zneo 9757 |
| [Apostol] p. 29 | Theorem I.35 | resqrtth 11818 sqrtthi 11907 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 9316 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwodc 12837 |
| [Apostol] p. 363 | Remark | absgt0api 11934 |
| [Apostol] p. 363 | Example | abssubd 11981 abssubi 11938 |
| [ApostolNT] p. 8 | Definition | df-ppi 16254 |
| [ApostolNT] p. 14 | Definition | df-dvds 12579 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 12595 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 12619 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 12615 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 12609 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 12611 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 12596 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 12597 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 12602 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 12636 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 12638 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 12640 |
| [ApostolNT] p. 15 | Definition | dfgcd2 12815 |
| [ApostolNT] p. 16 | Definition | isprm2 12919 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 12894 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 13403 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 12774 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 12816 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 12818 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 12788 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 12781 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 12947 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 12949 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 13175 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 12715 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 12861 |
| [ApostolNT] p. 25 | Definition | df-phi 13017 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 13047 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 13028 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 13032 |
| [ApostolNT] p. 38 | Remark | df-sgm 16255 |
| [ApostolNT] p. 38 | Definition | df-sgm 16255 |
| [ApostolNT] p. 75 | Definition | df-cht 16253 |
| [ApostolNT] p. 104 | Definition | congr 12902 |
| [ApostolNT] p. 106 | Remark | dvdsval3 12582 |
| [ApostolNT] p. 106 | Definition | moddvds 12590 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 12669 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 12670 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 10798 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modqmul12d 10835 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modqexp 11124 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 12614 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 12905 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 13229 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 12907 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 13039 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 13058 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 13040 |
| [ApostolNT] p. 179 | Definition | df-lgs 16339 lgsprme0 16383 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 16384 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 16360 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 16375 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 16426 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 16445 2lgsoddprm 16454 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 16410 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 16421 |
| [ApostolNT] p. 188 | Definition | df-lgs 16339 lgs1 16385 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 16376 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 16378 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 16386 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 16387 |
| [Bauer] p. 482 | Section 1.2 | pm2.01 625 pm2.65 669 |
| [Bauer] p. 483 | Theorem 1.3 | acexmid 6087 onsucelsucexmidlem 4678 |
| [Bauer], p. 481 | Section 1.1 | pwtrufal 17249 |
| [Bauer], p. 483 | Definition | n0rf 3534 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 16229 2irrexpqap 16231 |
| [Bauer], p. 485 | Theorem 2.1 | exmidssfi 7252 ssfiexmid 7184 ssfiexmidt 7186 |
| [Bauer], p. 493 | Section 5.1 | ivthdich 15896 |
| [Bauer], p. 494 | Theorem 5.5 | ivthinc 15886 |
| [BauerHanson], p. 27 | Proposition 5.2 | cnstab 8981 |
| [BauerSwan], p. 3 | Definition on page 14:3 | enumct 7461 |
| [BauerSwan], p. 14 | Remark | 0ct 7453 ctm 7455 |
| [BauerSwan], p. 14 | Proposition 2.6 | subctctexmid 17252 |
| [BauerTaylor], p. 32 | Lemma 6.16 | prarloclem 7874 |
| [BauerTaylor], p. 50 | Lemma 11.4 | subhalfnqq 7787 |
| [BauerTaylor], p. 52 | Proposition 11.15 | prarloc 7876 |
| [BauerTaylor], p. 53 | Lemma 11.16 | addclpr 7910 addlocpr 7909 |
| [BauerTaylor], p. 55 | Proposition 12.7 | appdivnq 7936 |
| [BauerTaylor], p. 56 | Lemma 12.8 | prmuloc 7939 |
| [BauerTaylor], p. 56 | Lemma 12.9 | mullocpr 7944 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 20 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2089 |
| [BellMachover] p. 460 | Notation | df-mo 2090 |
| [BellMachover] p. 460 | Definition | mo3 2141 mo3h 2140 |
| [BellMachover] p. 462 | Theorem 1.1 | bm1.1 2223 |
| [BellMachover] p. 463 | Theorem 1.3ii | bm1.3ii 4256 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 4316 |
| [BellMachover] p. 466 | Axiom Union | axun2 4582 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 4691 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 4531 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 4694 |
| [BellMachover] p. 471 | Problem 2.5(ii) | bm2.5ii 4645 |
| [BellMachover] p. 471 | Definition of Lim | df-ilim 4516 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 4738 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 4763 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1480 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1478 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1481 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1476 |
| [Bollobas] p. 1 | Section I.1 | df-edg 16521 isuhgropm 16544 isusgropen 16628 isuspgropen 16627 |
| [Bollobas] p. 2 | Section I.1 | df-subgr 16717 uhgrspansubgr 16740 |
| [Bollobas] p. 4 | Definition | df-wlks 16781 |
| [Bollobas] p. 5 | Definition | df-trls 16844 |
| [Bollobas] p. 7 | Section I.1 | df-ushgrm 16533 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-mgm 13734 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-sgrp 13775 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 13788 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 14408 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 14338 |
| [BourbakiEns] p. | Proposition 8 | fcof1 5992 fcofo 5993 |
| [BourbakiTop1] p. | Remark | xnegmnf 10247 xnegpnf 10246 |
| [BourbakiTop1] p. | Remark | rexneg 10248 |
| [BourbakiTop1] p. | Proposition | ishmeo 15547 |
| [BourbakiTop1] p. | Property V_i | ssnei2 15400 |
| [BourbakiTop1] p. | Property V_ii | innei 15406 |
| [BourbakiTop1] p. | Property V_iv | neissex 15408 |
| [BourbakiTop1] p. | Proposition 1 | neipsm 15397 neiss 15393 |
| [BourbakiTop1] p. | Proposition 2 | cnptopco 15465 |
| [BourbakiTop1] p. | Proposition 4 | imasnopn 15542 |
| [BourbakiTop1] p. | Property V_iii | elnei 15395 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 15241 |
| [Bruck] p. 1 | Section I.1 | df-mgm 13734 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 13775 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3m 13962 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 4195 |
| [Church] p. 129 | Section II.24 | df-ifp 991 dfifp2dc 994 |
| [Cohen] p. 301 | Remark | relogoprlem 16115 |
| [Cohen] p. 301 | Property 2 | relogmul 16116 relogmuld 16131 |
| [Cohen] p. 301 | Property 3 | relogdiv 16117 relogdivd 16132 |
| [Cohen] p. 301 | Property 4 | relogexp 16119 |
| [Cohen] p. 301 | Property 1a | log1 16112 |
| [Cohen] p. 301 | Property 1b | loge 16113 |
| [Cohen4] p. 348 | Observation | relogbcxpbap 16218 |
| [Cohen4] p. 352 | Definition | rpelogb 16202 |
| [Cohen4] p. 361 | Property 2 | rprelogbmul 16208 |
| [Cohen4] p. 361 | Property 3 | logbrec 16213 rprelogbdiv 16210 |
| [Cohen4] p. 361 | Property 4 | rplogbreexp 16206 |
| [Cohen4] p. 361 | Property 6 | relogbexpap 16211 |
| [Cohen4] p. 361 | Property 1(a) | rplogbid1 16200 |
| [Cohen4] p. 361 | Property 1(b) | rplogb1 16201 |
| [Cohen4] p. 367 | Property | rplogbchbase 16203 |
| [Cohen4] p. 377 | Property 2 | logblt 16215 |
| [Crosilla] p. | Axiom 1 | ax-ext 2220 |
| [Crosilla] p. | Axiom 2 | ax-pr 4348 |
| [Crosilla] p. | Axiom 3 | ax-un 4580 |
| [Crosilla] p. | Axiom 4 | ax-nul 4261 |
| [Crosilla] p. | Axiom 5 | ax-iinf 4737 |
| [Crosilla] p. | Axiom 6 | ru 3050 |
| [Crosilla] p. | Axiom 8 | ax-pow 4313 |
| [Crosilla] p. | Axiom 9 | ax-setind 4686 |
| [Crosilla], p. | Axiom 6 | ax-sep 4251 |
| [Crosilla], p. | Axiom 7 | ax-coll 4248 |
| [Crosilla], p. | Axiom 7' | repizf 4249 |
| [Crosilla], p. | Theorem is stated | ordtriexmid 4670 |
| [Crosilla], p. | Axiom of choice implies instances | acexmid 6087 |
| [Crosilla], p. | Definition of ordinal | df-iord 4513 |
| [Crosilla], p. | Theorem "Foundation implies instances of EM" | regexmid 4684 |
| [Diestel] p. 4 | Section 1.1 | df-subgr 16717 uhgrspansubgr 16740 |
| [Diestel] p. 27 | Section 1.10 | df-ushgrm 16533 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3222 |
| [Eisenberg] p. 82 | Definition 6.3 | df-iom 4740 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 6929 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 4260 |
| [Enderton] p. 19 | Definition | df-tp 3717 |
| [Enderton] p. 26 | Exercise 5 | unissb 3965 |
| [Enderton] p. 26 | Exercise 10 | pwel 4360 |
| [Enderton] p. 28 | Exercise 7(b) | pwunim 4433 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1m 4082 iinin2m 4081 iunin1 4077 iunin2 4076 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2m 4080 iundif2ss 4078 |
| [Enderton] p. 33 | Exercise 23 | iinuniss 4095 |
| [Enderton] p. 33 | Exercise 25 | iununir 4096 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 4103 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 4628 iunpwss 4104 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 4359 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4331 |
| [Enderton] p. 41 | Lemma 3D | opeluu 4598 rnex 5052 rnexg 5049 |
| [Enderton] p. 41 | Exercise 8 | dmuni 4993 rnuni 5202 |
| [Enderton] p. 42 | Definition of a function | dffun7 5407 dffun8 5408 |
| [Enderton] p. 43 | Definition of function value | funfvdm2 5770 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 5445 |
| [Enderton] p. 44 | Definition (d) | dfima2 5131 dfima3 5132 |
| [Enderton] p. 47 | Theorem 3H | fvco2 5777 |
| [Enderton] p. 49 | Axiom of Choice (first form) | df-ac 7568 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 5970 |
| [Enderton] p. 52 | Definition | df-map 6929 |
| [Enderton] p. 53 | Exercise 21 | coass 5309 |
| [Enderton] p. 53 | Exercise 27 | dmco 5299 |
| [Enderton] p. 53 | Exercise 14(a) | funin 5455 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 5166 |
| [Enderton] p. 54 | Remark | ixpf 7008 ixpssmap 7020 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 6987 |
| [Enderton] p. 56 | Theorem 3M | erref 6832 |
| [Enderton] p. 57 | Lemma 3N | erthi 6860 |
| [Enderton] p. 57 | Definition | df-ec 6814 |
| [Enderton] p. 58 | Definition | df-qs 6818 |
| [Enderton] p. 60 | Theorem 3Q | th3q 6919 th3qcor 6918 th3qlem1 6916 th3qlem2 6917 |
| [Enderton] p. 61 | Exercise 35 | df-ec 6814 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 4990 |
| [Enderton] p. 68 | Definition of successor | df-suc 4518 |
| [Enderton] p. 71 | Definition | df-tr 4232 dftr4 4236 |
| [Enderton] p. 72 | Theorem 4E | unisuc 4560 unisucg 4561 |
| [Enderton] p. 73 | Exercise 6 | unisuc 4560 unisucg 4561 |
| [Enderton] p. 73 | Exercise 5(a) | truni 4245 |
| [Enderton] p. 73 | Exercise 5(b) | trint 4246 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 6752 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 6754 onasuc 6744 |
| [Enderton] p. 79 | Definition of operation value | df-ov 6091 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 6753 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 6755 onmsuc 6751 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 6763 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 6756 nnacom 6762 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 6764 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 6765 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 6767 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 6757 nnmsucr 6766 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 6806 |
| [Enderton] p. 129 | Definition | df-en 7029 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 6039 |
| [Enderton] p. 133 | Exercise 1 | xpomen 13343 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | phpm 7173 |
| [Enderton] p. 136 | Corollary 6E | nneneq 7164 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 7152 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 7580 |
| [Enderton] p. 143 | Theorem 6J | dju0en 7576 dju1en 7575 |
| [Enderton] p. 144 | Corollary 6K | undif2ss 3603 |
| [Enderton] p. 145 | Figure 38 | ffoss 5675 |
| [Enderton] p. 145 | Definition | df-dom 7030 |
| [Enderton] p. 146 | Example 1 | domen 7041 domeng 7042 |
| [Enderton] p. 146 | Example 3 | nndomo 7171 |
| [Enderton] p. 149 | Theorem 6L(c) | xpdom1 7139 xpdom1g 7137 xpdom2g 7136 |
| [Enderton] p. 168 | Definition | df-po 4443 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 4575 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 4536 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 4692 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 4539 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 4665 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 4638 |
| [Enderton] p. 194 | Remark | onprc 4701 |
| [Enderton] p. 194 | Exercise 16 | suc11 4707 |
| [Enderton] p. 197 | Definition | df-card 7530 |
| [Enderton] p. 200 | Exercise 25 | tfis 4732 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 4703 |
| [Enderton] p. 207 | Exercise 34 | opthreg 4705 |
| [Enderton] p. 208 | Exercise 35 | suc11g 4706 |
| [Geuvers], p. 1 | Remark | expap0 11026 |
| [Geuvers], p. 6 | Lemma 2.13 | mulap0r 8951 |
| [Geuvers], p. 6 | Lemma 2.15 | mulap0 8990 |
| [Geuvers], p. 9 | Lemma 2.35 | msqge0 8952 |
| [Geuvers], p. 9 | Definition 3.1(2) | ax-arch 8304 |
| [Geuvers], p. 10 | Lemma 3.9 | maxcom 11991 |
| [Geuvers], p. 10 | Lemma 3.10 | maxle1 11999 maxle2 12000 |
| [Geuvers], p. 10 | Lemma 3.11 | maxleast 12001 |
| [Geuvers], p. 10 | Lemma 3.12 | maxleb 12004 |
| [Geuvers], p. 11 | Definition 3.13 | dfabsmax 12005 |
| [Geuvers], p. 17 | Definition 6.1 | df-ap 8918 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 7720 enqer 7731 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nqqs 7724 df-nqqs 7721 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 7717 df-plqqs 7722 |
| [Gleason] p. 119 | Proposition 9-2.4 | df-mpq 7718 df-mqqs 7723 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 7725 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnqq 7781 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 7784 ltbtwnnq 7789 ltbtwnnqq 7788 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanqg 7773 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnqg 7774 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 7910 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addassprg 7952 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcomprg 7951 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 7970 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 7986 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltaprg 7992 ltaprlem 7991 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanprg 7989 |
| [Gleason] p. 124 | Proposition 9-3.7 | mulclpr 7945 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 7965 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulassprg 7954 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcomprg 7953 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrprg 7961 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 8011 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 8099 enrer 8108 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 8104 df-1r 8105 df-nr 8100 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 8102 df-plr 8101 negexsr 8145 recexsrlem 8147 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 8103 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 9298 creur 9297 cru 8938 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 8296 axcnre 8254 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 11644 crimd 11764 crimi 11724 crre 11643 crred 11763 crrei 11723 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 11646 remimd 11729 |
| [Gleason] p. 133 | Definition 10.36 | absval2 11844 absval2d 11973 absval2i 11932 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 11670 cjaddd 11752 cjaddi 11719 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 11671 cjmuld 11753 cjmuli 11720 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 11669 cjcjd 11730 cjcji 11702 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 11668 cjreb 11652 cjrebd 11733 cjrebi 11705 cjred 11758 rere 11651 rereb 11649 rerebd 11732 rerebi 11704 rered 11756 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 11677 addcjd 11744 addcji 11714 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 11788 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 11839 abscjd 11978 abscji 11936 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 11851 abs00d 11974 abs00i 11933 absne0d 11975 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 11884 releabsd 11979 releabsi 11937 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 11856 absmuld 11982 absmuli 11939 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 11842 sqabsaddi 11940 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 11892 abstrid 11984 abstrii 11943 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 10996 exp0 11000 expp1 11003 expp1d 11132 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | expadd 11038 expaddd 11133 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 16162 cxpmuld 16189 expmul 11041 expmuld 11134 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulexp 11035 mulexpd 11146 rpmulcxp 16159 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 10429 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 12116 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 12118 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 12117 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 12121 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 12114 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 12110 climcj 12111 climim 12113 climre 12112 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 8371 df-xr 8370 ltxr 10193 |
| [Gleason] p. 180 | Theorem 12-5.3 | climcau 12137 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 10755 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 14990 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 15607 xmet0 15606 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 15614 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 15616 mstri 15716 xmettri 15615 xmstri 15715 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 15522 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 15754 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn2 12100 addcncntop 15805 mulcn2 12102 mulcncntop 15807 subcn2 12101 subcncntop 15806 |
| [Gleason] p. 295 | Remark | bcval3 11210 bcval4 11211 |
| [Gleason] p. 295 | Equation 2 | bcpasc 11225 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 11208 df-bc 11207 |
| [Gleason] p. 296 | Remark | bcn0 11214 bcnn 11216 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 12275 |
| [Gleason] p. 308 | Equation 2 | ef0 12463 |
| [Gleason] p. 308 | Equation 3 | efcj 12464 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 12469 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 12473 |
| [Gleason] p. 310 | Equation 14 | sinadd 12527 |
| [Gleason] p. 310 | Equation 15 | cosadd 12528 |
| [Gleason] p. 311 | Equation 17 | sincossq 12539 |
| [Gleason] p. 311 | Equation 18 | cosbnd 12544 sinbnd 12543 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 12444 |
| [Golan] p. 1 | Remark | srgisid 14396 |
| [Golan] p. 1 | Definition | df-srg 14374 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 20 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1502 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 13874 mndideu 13797 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 13901 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 13930 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 13941 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3me 13963 |
| [Heyting] p. 127 | Axiom #1 | ax1hfs 17348 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1472 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1473 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1475 |
| [HoTT], p. | Lemma 10.4.1 | exmidontriim 7587 |
| [HoTT], p. | Theorem 7.2.6 | nndceq 6777 |
| [HoTT], p. | Exercise 11.10 | neapmkv 17342 |
| [HoTT], p. | Exercise 11.11 | mulap0bd 8993 |
| [HoTT], p. | Section 11.2.1 | df-iltp 7843 df-imp 7842 df-iplp 7841 df-reap 8911 |
| [HoTT], p. | Theorem 11.2.4 | recapb 9009 rerecapb 9181 |
| [HoTT], p. | Corollary 3.9.2 | uchoice 6375 |
| [HoTT], p. | Theorem 11.2.12 | cauappcvgpr 8035 |
| [HoTT], p. | Corollary 11.4.3 | conventions 16957 |
| [HoTT], p. | Exercise 11.6(i) | dcapnconst 17335 dceqnconst 17334 |
| [HoTT], p. | Corollary 11.2.13 | axcaucvg 8273 caucvgpr 8055 caucvgprpr 8085 caucvgsr 8175 |
| [HoTT], p. | Definition 11.2.1 | df-inp 7839 |
| [HoTT], p. | Exercise 11.6(ii) | nconstwlpo 17340 |
| [HoTT], p. | Proposition 11.2.3 | df-iso 4444 ltpopr 7968 ltsopr 7969 |
| [HoTT], p. | Definition 11.2.7(v) | apsym 8942 reapcotr 8934 reapirr 8913 |
| [HoTT], p. | Definition 11.2.7(vi) | 0lt1 8460 gt0add 8909 leadd1 8765 lelttr 8420 lemul1a 9196 lenlt 8407 ltadd1 8764 ltletr 8421 ltmul1 8928 reaplt 8924 |
| [Huneke] p. 2 | Statement | df-clwwlknon 16890 |
| [Jech] p. 4 | Definition of class | cv 1401 cvjust 2233 |
| [Jech] p. 78 | Note | opthprc 4828 |
| [KalishMontague] p. 81 | Note 1 | ax-i9 1583 |
| [Kreyszig] p. 3 | Property M1 | metcl 15596 xmetcl 15595 |
| [Kreyszig] p. 4 | Property M2 | meteq0 15603 |
| [Kreyszig] p. 12 | Equation 5 | muleqadd 9006 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 15685 |
| [Kreyszig] p. 19 | Remark | mopntopon 15686 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 15731 mopnm 15691 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 15729 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 15734 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 15756 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 15456 |
| [Kreyszig] p. 51 | Equation 2 | lmodvneg1 14775 |
| [Kreyszig] p. 51 | Equation 1a | lmod0vs 14766 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 14767 |
| [Kunen] p. 10 | Axiom 0 | a9e 1748 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 4250 |
| [Kunen] p. 24 | Definition 10.24 | mapval 6939 mapvalg 6937 |
| [Kunen] p. 31 | Definition 10.24 | mapex 6933 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4022 |
| [Lang] p. 3 | Statement | lidrideqd 13759 mndbn0 13802 |
| [Lang] p. 3 | Definition | df-mnd 13788 |
| [Lang] p. 4 | Definition of a (finite) product | gzsumsplit1r 13773 |
| [Lang] p. 5 | Equation | gzsumreidx 14230 |
| [Lang] p. 6 | Definition | mulgnn0gzsum 13989 |
| [Lang] p. 7 | Definition | dfgrp2e 13891 |
| [Lang2] p. 3 | Notations | df-ind 9303 |
| [Levy] p. 338 | Axiom | df-clab 2225 df-clel 2234 df-cleq 2231 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1472 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1473 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1475 |
| [Margaris] p. 40 | Rule C | exlimiv 1651 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | condc 865 |
| [Margaris] p. 49 | Definition | dfbi2 392 dfordc 904 exalim 1555 |
| [Margaris] p. 51 | Theorem 1 | idALT 20 |
| [Margaris] p. 56 | Theorem 3 | syld 45 |
| [Margaris] p. 60 | Theorem 8 | jcn 661 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1691 r19.2m 3614 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 1607 19.3h 1606 rr19.3v 2965 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 1531 |
| [Margaris] p. 89 | Theorem 19.6 | alexdc 1672 alexim 1698 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1552 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 1643 spsbe 1895 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 1697 19.9h 1696 19.9v 1924 exlimd 1650 |
| [Margaris] p. 89 | Theorem 19.11 | excom 1716 excomim 1715 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 1717 r19.12 2657 |
| [Margaris] p. 90 | Theorem 19.14 | exnalim 1699 |
| [Margaris] p. 90 | Theorem 19.15 | albi 1521 ralbi 2683 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 1608 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 1609 |
| [Margaris] p. 90 | Theorem 19.18 | exbi 1657 rexbi 2684 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 1718 |
| [Margaris] p. 90 | Theorem 19.20 | alim 1510 alimd 1574 alimdh 1520 alimdv 1932 ralimdaa 2616 ralimdv 2618 ralimdva 2617 ralimdvva 2619 sbcimdv 3117 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21-2 1719 19.21 1636 19.21bi 1611 19.21h 1610 19.21ht 1634 19.21t 1635 19.21v 1926 alrimd 1663 alrimdd 1662 alrimdh 1532 alrimdv 1929 alrimi 1575 alrimih 1522 alrimiv 1927 alrimivv 1928 r19.21 2626 r19.21be 2641 r19.21bi 2638 r19.21t 2625 r19.21v 2627 ralrimd 2628 ralrimdv 2629 ralrimdva 2630 ralrimdvv 2634 ralrimdvva 2635 ralrimi 2621 ralrimiv 2622 ralrimiva 2623 ralrimivv 2631 ralrimivva 2632 ralrimivvva 2633 ralrimivw 2624 rexlimi 2661 |
| [Margaris] p. 90 | Theorem 19.22 | 2alimdv 1934 2eximdv 1935 exim 1652 eximd 1665 eximdh 1664 eximdv 1933 rexim 2644 reximdai 2648 reximddv 2653 reximddv2 2655 reximdv 2651 reximdv2 2649 reximdva 2652 reximdvai 2650 reximi2 2646 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 1730 19.23bi 1645 19.23h 1551 19.23ht 1550 19.23t 1729 19.23v 1936 19.23vv 1937 exlimd2 1648 exlimdh 1649 exlimdv 1872 exlimdvv 1953 exlimi 1647 exlimih 1646 exlimiv 1651 exlimivv 1952 r19.23 2659 r19.23v 2660 rexlimd 2665 rexlimdv 2667 rexlimdv3a 2670 rexlimdva 2668 rexlimdva2 2671 rexlimdvaa 2669 rexlimdvv 2675 rexlimdvva 2676 rexlimdvw 2672 rexlimiv 2662 rexlimiva 2663 rexlimivv 2674 |
| [Margaris] p. 90 | Theorem 19.24 | i19.24 1692 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1679 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26-2 1535 19.26-3an 1536 19.26 1534 r19.26-2 2680 r19.26-3 2681 r19.26 2677 r19.26m 2682 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 1614 19.27h 1613 19.27v 1955 r19.27av 2686 r19.27m 3623 r19.27mv 3624 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 1616 19.28h 1615 19.28v 1956 r19.28av 2687 r19.28m 3617 r19.28mv 3620 rr19.28v 2966 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1673 19.29r 1674 19.29r2 1675 19.29x 1676 r19.29 2688 r19.29d2r 2695 r19.29r 2689 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30dc 1680 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31r 1733 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32dc 1731 19.32r 1732 r19.32r 2697 r19.32vdc 2700 r19.32vr 2699 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33 1537 19.33b2 1682 19.33bdc 1683 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1736 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35-1 1677 19.35i 1678 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36-1 1725 19.36aiv 1957 19.36i 1724 r19.36av 2702 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37-1 1726 19.37aiv 1727 r19.37 2703 r19.37av 2704 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1728 |
| [Margaris] p. 90 | Theorem 19.39 | i19.39 1693 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1685 19.40 1684 r19.40 2705 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 1738 19.41h 1737 19.41v 1958 19.41vv 1959 19.41vvv 1960 19.41vvvv 1961 r19.41 2706 r19.41v 2707 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 1740 19.42h 1739 19.42v 1962 19.42vv 1967 19.42vvv 1968 19.42vvvv 1969 r19.42v 2708 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1681 r19.43 2709 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 1734 r19.44av 2710 r19.44mv 3622 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 1735 r19.45av 2711 r19.45mv 3621 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2111 |
| [Megill] p. 444 | Axiom C5 | ax-17 1579 |
| [Megill] p. 445 | Lemma L12 | alequcom 1568 ax-10 1558 |
| [Megill] p. 446 | Lemma L17 | equtrr 1762 |
| [Megill] p. 446 | Lemma L19 | hbnae 1773 |
| [Megill] p. 447 | Remark 9.1 | df-sb 1816 sbid 1827 |
| [Megill] p. 448 | Scheme C5' | ax-4 1563 |
| [Megill] p. 448 | Scheme C6' | ax-7 1501 |
| [Megill] p. 448 | Scheme C8' | ax-8 1557 |
| [Megill] p. 448 | Scheme C9' | ax-i12 1560 |
| [Megill] p. 448 | Scheme C11' | ax-10o 1768 |
| [Megill] p. 448 | Scheme C12' | ax-13 2211 |
| [Megill] p. 448 | Scheme C13' | ax-14 2212 |
| [Megill] p. 448 | Scheme C15' | ax-11o 1876 |
| [Megill] p. 448 | Scheme C16' | ax-16 1867 |
| [Megill] p. 448 | Theorem 9.4 | dral1 1783 dral2 1784 drex1 1851 drex2 1785 drsb1 1852 drsb2 1894 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2047 sbequ 1893 sbid2v 2056 |
| [Megill] p. 450 | Example in Appendix | hba1 1593 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 20 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3135 rspsbca 3136 stdpc4 1828 |
| [Mendelson] p. 69 | Axiom 5 | ra5 3141 stdpc5 1637 |
| [Mendelson] p. 81 | Rule C | exlimiv 1651 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 1755 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 1823 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 3559 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 3560 |
| [Mendelson] p. 231 | Exercise 4.10(n) | inssun 3471 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 3521 |
| [Mendelson] p. 231 | Exercise 4.10(q) | inssddif 3472 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddifnel 3360 |
| [Mendelson] p. 231 | Definition of union | unssin 3470 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 4624 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 3934 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 4429 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4430 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssunim 4431 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 3955 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 4911 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 5311 |
| [Mendelson] p. 246 | Definition of successor | df-suc 4518 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 7151 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 7125 xpsneng 7126 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 7131 xpcomeng 7132 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 7134 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 7128 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 6931 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 7106 mapsnend 7105 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 7157 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 7156 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 6972 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 7107 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 7579 djucomen 7578 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 7577 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 6745 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 3453 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 4865 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 4866 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 4194 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 5306 coi2 5307 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 4997 rn0 5040 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5195 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 4886 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxpm 5004 rnxpm 5220 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 4857 xp0 5210 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 5149 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 5146 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 5144 imaexg 5143 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 5140 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 5841 funfvop 5824 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 5747 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 5757 |
| [Monk1] p. 43 | Theorem 4.6 | funun 5425 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 5977 dff13f 5979 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 5943 funrnex 6347 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 5971 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 5274 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 3986 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 6393 df-1st 6378 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 6394 df-2nd 6379 |
| [Monk2] p. 105 | Axiom C4 | ax-5 1500 |
| [Monk2] p. 105 | Axiom C7 | ax-8 1557 |
| [Monk2] p. 105 | Axiom C8 | ax-11 1559 ax-11o 1876 |
| [Monk2] p. 105 | Axiom (C8) | ax11v 1880 |
| [Monk2] p. 109 | Lemma 12 | ax-7 1501 |
| [Monk2] p. 109 | Lemma 15 | equvin 1916 equvini 1811 eqvinop 4385 |
| [Monk2] p. 113 | Axiom C5-1 | ax-17 1579 |
| [Monk2] p. 113 | Axiom C5-2 | hbn1 1704 |
| [Monk2] p. 113 | Axiom C5-3 | ax-7 1501 |
| [Monk2] p. 114 | Lemma 22 | hba1 1593 |
| [Monk2] p. 114 | Lemma 23 | hbia1 1605 nfia1 1633 |
| [Monk2] p. 114 | Lemma 24 | hba2 1604 nfa2 1632 |
| [Moschovakis] p. 2 | Chapter 2 | df-stab 843 dftest 17349 |
| [Munkres] p. 77 | Example 2 | distop 15328 |
| [Munkres] p. 78 | Definition of basis | df-bases 15286 isbasis3g 15289 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 13672 tgval2 15294 |
| [Munkres] p. 79 | Remark | tgcl 15307 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 15301 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 15322 tgss3 15321 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 15323 basgen2 15324 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 15413 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 15355 topcld 15352 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 15356 |
| [Munkres] p. 94 | Definition of closure | clsval 15354 |
| [Munkres] p. 94 | Definition of interior | ntrval 15353 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 15431 iscn 15440 iscn2 15443 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 15473 cncnp2m 15474 cncnpi 15471 df-cnp 15432 iscnp 15442 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 15757 |
| [Pierik], p. 8 | Section 2.2.1 | dfrex2fin 7214 |
| [Pierik], p. 9 | Definition 2.4 | df-womni 7510 |
| [Pierik], p. 9 | Definition 2.5 | df-markov 7498 omniwomnimkv 7513 |
| [Pierik], p. 10 | Section 2.3 | dfdif3 3339 |
| [Pierik], p. 14 | Definition 3.1 | df-omni 7481 exmidomniim 7487 finomni 7486 |
| [Pierik], p. 15 | Section 3.1 | df-nninf 7466 |
| [Pradic2025], p. 2 | Section 1.1 | nnnninfen 17287 |
| [PradicBrown2022], p. 1 | Theorem 1 | exmidsbthr 17291 |
| [PradicBrown2022], p. 2 | Remark | exmidpw 7221 |
| [PradicBrown2022], p. 2 | Proposition 1.1 | exmidfodomrlemim 7559 |
| [PradicBrown2022], p. 2 | Proposition 1.2 | exmidfodomrlemr 7560 exmidfodomrlemrALT 7561 |
| [PradicBrown2022], p. 4 | Lemma 3.2 | fodjuomni 7495 |
| [PradicBrown2022], p. 5 | Lemma 3.4 | peano3nninf 17273 peano4nninf 17272 |
| [PradicBrown2022], p. 5 | Lemma 3.5 | nninfall 17275 |
| [PradicBrown2022], p. 5 | Theorem 3.6 | nninfsel 17283 |
| [PradicBrown2022], p. 5 | Corollary 3.7 | nninfomni 17285 |
| [PradicBrown2022], p. 5 | Definition 3.3 | nnsf 17271 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2225 rabid 2727 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2051 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2231 |
| [Quine] p. 19 | Definition 2.9 | df-v 2823 |
| [Quine] p. 34 | Theorem 5.1 | abeq2 2347 eqabb 2374 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2372 abid2 2361 abid2f 2418 |
| [Quine] p. 40 | Theorem 6.1 | sb5 1942 |
| [Quine] p. 40 | Theorem 6.2 | sb56 1940 sb6 1941 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2234 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2238 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2240 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3052 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3053 dfsbcq2 3054 |
| [Quine] p. 43 | Theorem 6.8 | vex 2824 |
| [Quine] p. 43 | Theorem 6.9 | isset 2828 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 2907 spcgv 2912 spcimgf 2905 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3063 spsbcd 3064 |
| [Quine] p. 44 | Theorem 6.12 | elex 2833 |
| [Quine] p. 44 | Theorem 6.13 | elab 2970 elabg 2972 elabgf 2968 |
| [Quine] p. 44 | Theorem 6.14 | noel 3525 |
| [Quine] p. 48 | Theorem 7.2 | snprc 3774 |
| [Quine] p. 48 | Definition 7.1 | df-pr 3716 df-sn 3715 |
| [Quine] p. 49 | Theorem 7.4 | snss 3850 snssg 3849 |
| [Quine] p. 49 | Theorem 7.5 | prss 3871 prssg 3872 |
| [Quine] p. 49 | Theorem 7.6 | prid1 3817 prid1g 3815 prid2 3818 prid2g 3816 snid 3740 snidg 3738 |
| [Quine] p. 51 | Theorem 7.12 | snexg 4323 snexprc 4325 |
| [Quine] p. 51 | Theorem 7.13 | prexg 4351 |
| [Quine] p. 53 | Theorem 8.2 | unisn 3951 unisng 3952 |
| [Quine] p. 53 | Theorem 8.3 | uniun 3954 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 3963 |
| [Quine] p. 54 | Theorem 8.7 | uni0 3962 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 5351 |
| [Quine] p. 56 | Definition 8.18 | dfiota2 5341 |
| [Quine] p. 57 | Theorem 8.19 | iotaval 5352 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 5356 |
| [Quine] p. 58 | Theorem 8.23 | euiotaex 5357 |
| [Quine] p. 58 | Definition 9.1 | df-op 3718 |
| [Quine] p. 61 | Theorem 9.5 | opabid 4400 opabidw 4401 opelopab 4416 opelopaba 4410 opelopabaf 4418 opelopabf 4419 opelopabg 4412 opelopabga 4407 opelopabgf 4414 oprabid 6120 |
| [Quine] p. 64 | Definition 9.11 | df-xp 4782 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 4784 |
| [Quine] p. 64 | Definition 9.15 | df-id 4440 |
| [Quine] p. 65 | Theorem 10.3 | fun0 5442 |
| [Quine] p. 65 | Theorem 10.4 | funi 5412 |
| [Quine] p. 65 | Theorem 10.5 | funsn 5432 funsng 5430 |
| [Quine] p. 65 | Definition 10.1 | df-fun 5382 |
| [Quine] p. 65 | Definition 10.2 | args 5159 dffv4g 5695 |
| [Quine] p. 68 | Definition 10.11 | df-fv 5388 fv2 5693 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 11183 nn0opth2d 11182 nn0opthd 11181 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 5469 funimaexg 5468 |
| [Roman] p. 18 | Part Preliminaries | df-rng 14338 |
| [Roman] p. 19 | Part Preliminaries | df-ring 14408 |
| [Rudin] p. 164 | Equation 27 | efcan 12467 |
| [Rudin] p. 164 | Equation 30 | efzval 12474 |
| [Rudin] p. 167 | Equation 48 | absefi 12560 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 17401 |
| [Sanford] p. 39 | Remark | ax-mp 5 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1475 |
| [Sanford] p. 39 | Rule 4 | mptxor 1473 |
| [Sanford] p. 40 | Rule 1 | mptnan 1472 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 5175 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 5177 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 5174 |
| [Schechter] p. 51 | Definition of transitivity | cotr 5172 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 14410 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 15326 |
| [Stoll] p. 13 | Definition of symmetric difference | symdif1 3496 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 3597 dif0 3596 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdirss 3612 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 3489 |
| [Stoll] p. 19 | Theorem 5.2(13') | indmss 3490 |
| [Stoll] p. 20 | Remark | invdif 3473 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 3719 |
| [Stoll] p. 43 | Definition | uniiun 4066 |
| [Stoll] p. 44 | Definition | intiin 4067 |
| [Stoll] p. 45 | Definition | df-iin 4015 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4014 |
| [Stoll] p. 176 | Theorem 3.4(27) | imandc 901 imanst 900 |
| [Stoll] p. 262 | Example 4.1 | symdif1 3496 |
| [Suppes] p. 22 | Theorem 2 | eq0 3540 |
| [Suppes] p. 22 | Theorem 4 | eqss 3263 eqssd 3265 eqssi 3264 |
| [Suppes] p. 23 | Theorem 5 | ss0 3563 ss0b 3562 |
| [Suppes] p. 23 | Theorem 6 | sstr 3256 |
| [Suppes] p. 25 | Theorem 12 | elin 3412 elun 3370 |
| [Suppes] p. 26 | Theorem 15 | inidm 3440 |
| [Suppes] p. 26 | Theorem 16 | in0 3557 |
| [Suppes] p. 27 | Theorem 23 | unidm 3372 |
| [Suppes] p. 27 | Theorem 24 | un0 3556 |
| [Suppes] p. 27 | Theorem 25 | ssun1 3392 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 3399 |
| [Suppes] p. 27 | Theorem 27 | unss 3403 |
| [Suppes] p. 27 | Theorem 28 | indir 3480 |
| [Suppes] p. 27 | Theorem 29 | undir 3481 |
| [Suppes] p. 28 | Theorem 32 | difid 3594 difidALT 3595 |
| [Suppes] p. 29 | Theorem 33 | difin 3468 |
| [Suppes] p. 29 | Theorem 34 | indif 3474 |
| [Suppes] p. 29 | Theorem 35 | undif1ss 3602 |
| [Suppes] p. 29 | Theorem 36 | difun2 3607 |
| [Suppes] p. 29 | Theorem 37 | difin0 3601 |
| [Suppes] p. 29 | Theorem 38 | disjdif 3599 |
| [Suppes] p. 29 | Theorem 39 | difundi 3483 |
| [Suppes] p. 29 | Theorem 40 | difindiss 3485 |
| [Suppes] p. 30 | Theorem 41 | nalset 4265 |
| [Suppes] p. 39 | Theorem 61 | uniss 3956 |
| [Suppes] p. 39 | Theorem 65 | uniop 4398 |
| [Suppes] p. 41 | Theorem 70 | intsn 4005 |
| [Suppes] p. 42 | Theorem 71 | intpr 4002 intprg 4003 |
| [Suppes] p. 42 | Theorem 73 | op1stb 4626 op1stbg 4627 |
| [Suppes] p. 42 | Theorem 78 | intun 4001 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4046 dfiun2g 4044 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4047 |
| [Suppes] p. 47 | Theorem 86 | elpw 3694 elpw2 4295 elpw2g 4294 elpwg 3696 |
| [Suppes] p. 47 | Theorem 87 | pwid 3707 |
| [Suppes] p. 47 | Theorem 89 | pw0 3862 |
| [Suppes] p. 48 | Theorem 90 | pwpw0ss 3930 |
| [Suppes] p. 52 | Theorem 101 | xpss12 4884 |
| [Suppes] p. 52 | Theorem 102 | xpindi 4917 xpindir 4918 |
| [Suppes] p. 52 | Theorem 103 | xpundi 4833 xpundir 4834 |
| [Suppes] p. 54 | Theorem 105 | elirrv 4697 |
| [Suppes] p. 58 | Theorem 2 | relss 4864 |
| [Suppes] p. 59 | Theorem 4 | eldm 4980 eldm2 4981 eldm2g 4979 eldmg 4978 |
| [Suppes] p. 59 | Definition 3 | df-dm 4786 |
| [Suppes] p. 60 | Theorem 6 | dmin 4991 |
| [Suppes] p. 60 | Theorem 8 | rnun 5199 |
| [Suppes] p. 60 | Theorem 9 | rnin 5200 |
| [Suppes] p. 60 | Definition 4 | dfrn2 4970 |
| [Suppes] p. 61 | Theorem 11 | brcnv 4965 brcnvg 4963 |
| [Suppes] p. 62 | Equation 5 | elcnv 4959 elcnv2 4960 |
| [Suppes] p. 62 | Theorem 12 | relcnv 5168 |
| [Suppes] p. 62 | Theorem 15 | cnvin 5198 |
| [Suppes] p. 62 | Theorem 16 | cnvun 5196 |
| [Suppes] p. 63 | Theorem 20 | co02 5304 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5054 |
| [Suppes] p. 63 | Definition 7 | df-co 4785 |
| [Suppes] p. 64 | Theorem 26 | cnvco 4967 |
| [Suppes] p. 64 | Theorem 27 | coass 5309 |
| [Suppes] p. 65 | Theorem 31 | resundi 5078 |
| [Suppes] p. 65 | Theorem 34 | elima 5134 elima2 5135 elima3 5136 elimag 5133 |
| [Suppes] p. 65 | Theorem 35 | imaundi 5203 |
| [Suppes] p. 66 | Theorem 40 | dminss 5205 |
| [Suppes] p. 66 | Theorem 41 | imainss 5206 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 5209 |
| [Suppes] p. 81 | Definition 34 | dfec2 6815 |
| [Suppes] p. 82 | Theorem 72 | elec 6853 elecg 6852 |
| [Suppes] p. 82 | Theorem 73 | erth 6858 erth2 6859 |
| [Suppes] p. 89 | Theorem 96 | map0b 6973 |
| [Suppes] p. 89 | Theorem 97 | map0 6977 map0g 6974 |
| [Suppes] p. 89 | Theorem 98 | mapsn 6978 mapsnd 6976 |
| [Suppes] p. 89 | Theorem 99 | mapss 6979 |
| [Suppes] p. 92 | Theorem 1 | enref 7057 enrefg 7056 |
| [Suppes] p. 92 | Theorem 2 | ensym 7074 ensymb 7073 ensymi 7075 |
| [Suppes] p. 92 | Theorem 3 | entr 7077 |
| [Suppes] p. 92 | Theorem 4 | unen 7111 |
| [Suppes] p. 94 | Theorem 15 | endom 7055 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 7071 |
| [Suppes] p. 94 | Theorem 17 | domtr 7078 |
| [Suppes] p. 95 | Theorem 18 | isbth 7291 |
| [Suppes] p. 98 | Exercise 4 | fundmen 7100 fundmeng 7101 |
| [Suppes] p. 98 | Exercise 6 | xpdom3m 7138 |
| [Suppes] p. 130 | Definition 3 | df-tr 4232 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 4637 |
| [Suppes] p. 134 | Definition 6 | df-suc 4518 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 4752 finds 4749 finds1 4751 finds2 4750 |
| [Suppes] p. 162 | Definition 5 | df-ltnqqs 7726 df-ltpq 7719 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 4537 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2220 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2231 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2234 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2233 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2256 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 6092 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3050 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 3730 elpr2 3731 elprg 3729 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 3725 elsn2 3743 elsn2g 3742 elsng 3724 velsn 3726 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 4373 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 3720 sneqr 3885 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 3728 dfsn2 3723 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 4585 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 4379 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 4357 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 4589 unexg 4591 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 3758 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 3936 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3226 df-un 3224 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 3949 uniprg 3950 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 4318 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 3757 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 4553 elsucg 4551 sstr2 3255 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 3373 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 3421 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 3386 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 3441 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 3478 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 3479 |
| [TakeutiZaring] p. 17 | Definition 5.9 | ssalel 3235 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 3690 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 3400 |
| [TakeutiZaring] p. 18 | Exercise 9 | df-ss 3233 dfss2 3237 sseqin2 3450 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3268 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 3451 inss2 3452 |
| [TakeutiZaring] p. 18 | Exercise 13 | nssr 3308 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 3944 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 4358 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 4365 |
| [TakeutiZaring] p. 20 | Definition | df-rab 2537 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 4262 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3222 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 3523 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 3594 difidALT 3595 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0rf 3534 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 4688 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 2823 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 4267 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 3561 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 4272 ssexg 4274 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 4269 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 4699 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 4690 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0im 3589 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 3354 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3ss 3492 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 3355 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 3363 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 2533 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 2534 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 4893 xpexg 4891 xpexgALT 6370 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 4783 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 5448 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 5612 fun11 5451 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 5391 svrelfun 5449 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 4969 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 4971 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 4788 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 4789 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 4785 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 5245 dfrel2 5241 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 4885 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 4896 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 4902 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 4916 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5093 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5070 opelresg 5072 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5086 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5089 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5094 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 5421 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 5289 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 5420 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 5613 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2131 |
| [TakeutiZaring] p. 26 | Definition 6.11 | df-fv 5388 fv3 5721 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 5329 cnvexg 5328 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 5051 dmexg 5048 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 5052 rnexg 5049 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnvm 5145 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | funfvex 5715 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1 5725 tz6.12 5726 tz6.12c 5728 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2 5689 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 5383 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 5384 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 5386 wfo 5378 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 5385 wf1 5377 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 5387 wf1o 5379 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 5809 eqfnfv2 5810 eqfnfv2f 5813 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 5778 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 5940 fnexALT 6344 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 5939 resfunexgALT 6341 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 5469 funimaexg 5468 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 4132 |
| [TakeutiZaring] p. 30 | Definition 6.21 | eliniseg 5160 iniseg 5162 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 4436 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 5389 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 6019 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 6020 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 6025 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 6027 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 6035 |
| [TakeutiZaring] p. 35 | Notation | wtr 4231 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | tz7.2 4501 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 4235 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 4725 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 4528 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 4532 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 4641 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 4515 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | ordon 4635 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 4701 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 4731 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 4233 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 4660 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 4636 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 3963 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 4518 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 4562 sucidg 4563 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 4650 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-ilim 4516 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 4655 ordelsuc 4654 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 4743 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 4744 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 4745 |
| [TakeutiZaring] p. 43 | Axiom 7 | omex 4742 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 4756 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 4748 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 4746 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 4747 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 3984 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintssm 4247 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 3985 |
| [TakeutiZaring] p. 44 | Exercise 6 | onintonm 4666 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 3971 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 6584 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfri1 6641 tfri1d 6611 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfri2 6642 tfri2d 6612 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfri3 6643 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 6578 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 6562 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oasuc 6742 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 6738 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 6735 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 6739 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 6787 nnaordi 6786 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4057 uniss2 3966 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordriexmid 6748 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 6758 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 6749 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0 6736 omsuc 6750 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnmcl 6759 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 6795 nnmordi 6794 |
| [TakeutiZaring] p. 67 | Definition 8.30 | oei0 6737 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 7538 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 7088 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 7164 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 7165 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 7031 isfi 7053 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 7135 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 6929 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2f1odc 7141 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 7154 |
| [Tarski] p. 67 | Axiom B5 | ax-4 1563 |
| [Tarski] p. 68 | Lemma 6 | equid 1753 |
| [Tarski] p. 69 | Lemma 7 | equcomi 1756 |
| [Tarski] p. 70 | Lemma 14 | spim 1791 spime 1794 spimeh 1792 spimh 1790 |
| [Tarski] p. 70 | Lemma 16 | ax-11 1559 ax-11o 1876 ax11i 1766 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 1941 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-17 1579 |
| [Tarski] p. 77 | Axiom B8 (p. 75) of system S2 | ax-13 2211 ax-14 2212 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 723 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 739 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 (Taut) | pm1.2 768 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 777 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 801 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 625 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 652 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 82 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | imim2 55 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | imim1 76 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1dc 849 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2185 syl 14 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 749 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 19 idALT 20 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmiddc 848 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 638 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13dc 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotrdc 855 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1dc 868 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | con3 651 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | condc 865 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18dc 867 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 724 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 787 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 626 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 630 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25dc 905 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26dc 919 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | pm2.27 40 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 780 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 781 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 816 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 817 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 815 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1010 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 790 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 788 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 789 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 53 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 750 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 751 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5dc 879 pm2.5gdc 878 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6dc 874 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 752 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 753 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 754 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 665 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 666 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 734 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54dc 903 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 737 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 738 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61dc 877 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 760 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 812 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 813 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 669 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 725 pm2.67 755 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521dc 881 pm2.521gdc 880 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 759 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 822 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68dc 906 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinvdc 927 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 818 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 819 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 821 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 820 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 823 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 824 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 77 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85dc 917 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 101 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 766 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 139 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11dc 970 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12dc 971 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13dc 972 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 765 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 264 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 265 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 705 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 347 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 261 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 262 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 109 simplimdc 872 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 110 simprimdc 871 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 345 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 346 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 700 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 605 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 333 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 331 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 332 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 767 pm3.44 727 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 344 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 610 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 797 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34bdc 883 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 171 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotbdc 884 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14dc 902 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 706 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 140 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 965 bitr 476 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 399 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 769 pm4.25 770 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 266 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 830 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 740 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 405 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 779 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 470 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 804 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 613 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 834 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1011 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 828 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42r 984 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 962 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 791 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 826 pm4.45 796 pm4.45im 334 |
| [WhiteheadRussell] p. 119 | Theorem *10.22 | 19.26 1534 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anordc 969 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imordc 909 imorr 733 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 319 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianordc 911 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52im 762 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53r 763 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54dc 914 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55dc 951 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 764 pm4.56 792 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | orandc 952 oranim 793 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | annimim 697 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62dc 910 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63dc 898 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64dc 912 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65r 698 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66dc 913 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67dc 899 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 393 pm4.71d 397 pm4.71i 395 pm4.71r 394 pm4.71rd 398 pm4.71ri 396 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 839 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 300 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 756 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 611 pm4.76 612 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 722 pm4.77 811 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78i 794 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79dc 915 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 719 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81dc 920 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 963 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83dc 964 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 236 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 237 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 240 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 248 impexp 263 pm4.87 563 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 609 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11dc 921 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12dc 922 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13dc 924 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14dc 923 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15dc 1438 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 840 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17dc 916 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbndc 1443 pm5.18dc 895 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 718 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 707 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xordc 1441 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3dc 1446 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24dc 1447 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2dc 907 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 479 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 249 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 242 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6dc 938 pm5.6r 939 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7dc 967 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 348 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 457 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 617 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 929 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 618 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 250 pm5.41 251 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 320 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 937 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 814 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54dc 930 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55dc 925 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 806 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62dc 958 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63dc 959 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71dc 974 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 244 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 179 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 975 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1688 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 1538 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1685 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 1951 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2089 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 2501 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 2502 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 2964 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3108 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 5360 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 5361 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2166 eupickbi 2169 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | df-fv 5388 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 7542 |
| [vandenDries] p. 43 | Theorem 62 | pellexlem1 16246 |
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