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Theorem List for Metamath Proof Explorer - 1201-1300   *Has distinct variable group(s)
TypeLabelDescription
Statement

Theorem3anbi2i 1201 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
(𝜑𝜓)       ((𝜒𝜑𝜃) ↔ (𝜒𝜓𝜃))

Theorem3anbi3i 1202 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)
(𝜑𝜓)       ((𝜒𝜃𝜑) ↔ (𝜒𝜃𝜓))

Theoremsyl3an 1203 A triple syllogism inference. (Contributed by NM, 13-May-2004.)
(𝜑𝜓)    &   (𝜒𝜃)    &   (𝜏𝜂)    &   ((𝜓𝜃𝜂) → 𝜁)       ((𝜑𝜒𝜏) → 𝜁)

Theoremsyl3anb 1204 A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)
(𝜑𝜓)    &   (𝜒𝜃)    &   (𝜏𝜂)    &   ((𝜓𝜃𝜂) → 𝜁)       ((𝜑𝜒𝜏) → 𝜁)

Theoremsyl3anbr 1205 A triple syllogism inference. (Contributed by NM, 29-Dec-2011.)
(𝜓𝜑)    &   (𝜃𝜒)    &   (𝜂𝜏)    &   ((𝜓𝜃𝜂) → 𝜁)       ((𝜑𝜒𝜏) → 𝜁)

Theoremsyl3an1 1206 A syllogism inference. (Contributed by NM, 22-Aug-1995.)
(𝜑𝜓)    &   ((𝜓𝜒𝜃) → 𝜏)       ((𝜑𝜒𝜃) → 𝜏)

Theoremsyl3an2 1207 A syllogism inference. (Contributed by NM, 22-Aug-1995.) (Proof shortened by Wolf Lammen, 26-Jun-2022.)
(𝜑𝜒)    &   ((𝜓𝜒𝜃) → 𝜏)       ((𝜓𝜑𝜃) → 𝜏)

Theoremsyl3an2OLD 1208 Obsolete version of syl3an2 1207 as of 26-Jun-2022. (Contributed by NM, 22-Aug-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
(𝜑𝜒)    &   ((𝜓𝜒𝜃) → 𝜏)       ((𝜓𝜑𝜃) → 𝜏)

Theoremsyl3an3 1209 A syllogism inference. (Contributed by NM, 22-Aug-1995.) (Proof shortened by Wolf Lammen, 26-Jun-2022.)
(𝜑𝜃)    &   ((𝜓𝜒𝜃) → 𝜏)       ((𝜓𝜒𝜑) → 𝜏)

Theoremsyl3an3OLD 1210 Obsolete version of syl3an3 1209 as of 26-Jun-2022. (Contributed by NM, 22-Aug-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
(𝜑𝜃)    &   ((𝜓𝜒𝜃) → 𝜏)       ((𝜓𝜒𝜑) → 𝜏)

Theorem3adantl1 1211 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
(((𝜑𝜓) ∧ 𝜒) → 𝜃)       (((𝜏𝜑𝜓) ∧ 𝜒) → 𝜃)

Theorem3adantl2 1212 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
(((𝜑𝜓) ∧ 𝜒) → 𝜃)       (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)

Theorem3adantl3 1213 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
(((𝜑𝜓) ∧ 𝜒) → 𝜃)       (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)

Theorem3adantr1 1214 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
((𝜑 ∧ (𝜓𝜒)) → 𝜃)       ((𝜑 ∧ (𝜏𝜓𝜒)) → 𝜃)

Theorem3adantr2 1215 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
((𝜑 ∧ (𝜓𝜒)) → 𝜃)       ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)

Theorem3adantr3 1216 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
((𝜑 ∧ (𝜓𝜒)) → 𝜃)       ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

Theoremad4ant123 1217 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜃)

Theoremad4ant123OLD 1218 Obsolete version of ad4ant123 1217 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜃)

Theoremad4ant124 1219 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)

Theoremad4ant124OLD 1220 Obsolete version of ad4ant124 1219 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃)

Theoremad4ant134 1221 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Theoremad4ant134OLD 1222 Obsolete version of ad4ant134 1221 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Theoremad4ant234 1223 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Theoremad4ant234OLD 1224 Obsolete version of ad4ant234 1223 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((((𝜏𝜑) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Theorem3adant1l 1225 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜑𝜓𝜒) → 𝜃)       (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)

Theorem3adant1lOLD 1226 Obsolete version of 3adant1l 1225 as of 23-Jun-2022. (Contributed by NM, 8-Jan-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)

Theorem3adant1r 1227 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜑𝜓𝜒) → 𝜃)       (((𝜑𝜏) ∧ 𝜓𝜒) → 𝜃)

Theorem3adant1rOLD 1228 Obsolete version of 3adant1r 1227 as of 23-Jun-2022. (Contributed by NM, 8-Jan-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       (((𝜑𝜏) ∧ 𝜓𝜒) → 𝜃)

Theorem3adant2l 1229 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 25-Jun-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜏𝜓) ∧ 𝜒) → 𝜃)

Theorem3adant2lOLD 1230 Obsolete version of 3adant2l 1229 as of 25-Jun-2022. (Contributed by NM, 8-Jan-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜏𝜓) ∧ 𝜒) → 𝜃)

Theorem3adant2r 1231 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 25-Jun-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)

Theorem3adant2rOLD 1232 Obsolete version of 3adant2r 1231 as of 25-Jun-2022. (Contributed by NM, 8-Jan-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)

Theorem3adant3l 1233 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 25-Jun-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑𝜓 ∧ (𝜏𝜒)) → 𝜃)

Theorem3adant3lOLD 1234 Obsolete version of 3adant3l 1233 as of 25-Jun-2022. (Contributed by NM, 8-Jan-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑𝜓 ∧ (𝜏𝜒)) → 𝜃)

Theorem3adant3r 1235 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 25-Jun-2022.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑𝜓 ∧ (𝜒𝜏)) → 𝜃)

Theorem3adant3rOLD 1236 Obsolete version of 3adant3r 1235 as of 25-Jun-2022. (Contributed by NM, 8-Jan-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑𝜓 ∧ (𝜒𝜏)) → 𝜃)

Theorem3adant3r1 1237 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜏𝜓𝜒)) → 𝜃)

Theorem3adant3r2 1238 Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)

Theorem3adant3r3 1239 Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
((𝜑𝜓𝜒) → 𝜃)       ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

((𝜑𝜒) → 𝜃)       (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)

((𝜑𝜒) → 𝜃)       (((𝜓𝜑𝜏) ∧ 𝜒) → 𝜃)

((𝜑𝜒) → 𝜃)       (((𝜓𝜏𝜑) ∧ 𝜒) → 𝜃)

((𝜑𝜒) → 𝜃)       ((𝜑 ∧ (𝜒𝜓𝜏)) → 𝜃)

((𝜑𝜒) → 𝜃)       ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

((𝜑𝜒) → 𝜃)       ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)

Theoremsimpl1 1246 Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
(((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)

Theoremsimpl1OLD 1247 Obsolete version of simpl1 1246 as of 23-Jun-2022. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
(((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)

Theoremsimpl2 1248 Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
(((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)

Theoremsimpl2OLD 1249 Obsolete version of simpl2 1248 as of 23-Jun-2022. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
(((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)

Theoremsimpl3 1250 Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
(((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)

Theoremsimpl3OLD 1251 Obsolete version of simpl3 1250 as of 23-Jun-2022. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
(((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)

Theoremsimpr1 1252 Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)

Theoremsimpr1OLD 1253 Obsolete version of simpr1 1252 as of 23-Jun-2022. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜓)

Theoremsimpr2 1254 Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜒)

Theoremsimpr2OLD 1255 Obsolete version of simpr2 1254 as of 23-Jun-2022. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜒)

Theoremsimpr3 1256 Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)

Theoremsimpr3OLD 1257 Obsolete version of simpr3 1256 as of 23-Jun-2022. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜃)

Theoremsimp1l 1258 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
(((𝜑𝜓) ∧ 𝜒𝜃) → 𝜑)

Theoremsimp1r 1259 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
(((𝜑𝜓) ∧ 𝜒𝜃) → 𝜓)

Theoremsimp2l 1260 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((𝜑 ∧ (𝜓𝜒) ∧ 𝜃) → 𝜓)

Theoremsimp2r 1261 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((𝜑 ∧ (𝜓𝜒) ∧ 𝜃) → 𝜒)

Theoremsimp3l 1262 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((𝜑𝜓 ∧ (𝜒𝜃)) → 𝜒)

Theoremsimp3r 1263 Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
((𝜑𝜓 ∧ (𝜒𝜃)) → 𝜃)

Theoremsimp11 1264 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
(((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)

Theoremsimp12 1265 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
(((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)

Theoremsimp13 1266 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
(((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)

Theoremsimp21 1267 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜓)

Theoremsimp22 1268 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜒)

Theoremsimp23 1269 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((𝜑 ∧ (𝜓𝜒𝜃) ∧ 𝜏) → 𝜃)

Theoremsimp31 1270 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜒)

Theoremsimp32 1271 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜃)

Theoremsimp33 1272 Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
((𝜑𝜓 ∧ (𝜒𝜃𝜏)) → 𝜏)

Theoremsimpll1 1273 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Theoremsimpll1OLD 1274 Obsolete version of simpll1 1273 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Theoremsimpll2 1275 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theoremsimpll2OLD 1276 Obsolete version of simpll2 1275 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theoremsimpll3 1277 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜒)

Theoremsimpll3OLD 1278 Obsolete version of simpll3 1277 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜒)

Theoremsimplr1 1279 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜑)

Theoremsimplr1OLD 1280 Obsolete version of simplr1 1279 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜑)

Theoremsimplr2 1281 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜓)

Theoremsimplr2OLD 1282 Obsolete version of simplr2 1281 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜓)

Theoremsimplr3 1283 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)

Theoremsimplr3OLD 1284 Obsolete version of simplr3 1283 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)

Theoremsimprl1 1285 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Theoremsimprl1OLD 1286 Obsolete version of simprl1 1285 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Theoremsimprl2 1287 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Theoremsimprl2OLD 1288 Obsolete version of simprl2 1287 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Theoremsimprl3 1289 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Theoremsimprl3OLD 1290 Obsolete version of simprl3 1289 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Theoremsimprr1 1291 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Theoremsimprr1OLD 1292 Obsolete version of simprr1 1291 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Theoremsimprr2 1293 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Theoremsimprr2OLD 1294 Obsolete version of simprr2 1293 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Theoremsimprr3 1295 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Theoremsimprr3OLD 1296 Obsolete version of simprr3 1295 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Theoremsimpl1l 1297 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏) → 𝜑)

Theoremsimpl1lOLD 1298 Obsolete version of simpl1l 1297 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏) → 𝜑)

Theoremsimpl1r 1299 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏) → 𝜓)

Theoremsimpl1rOLD 1300 Obsolete version of simpl1r 1299 as of 23-Jun-2022. (Contributed by NM, 9-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏) → 𝜓)

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