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

Theorem3exp1 1201 Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3expd 1202 Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp2 1203 Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theoremexp5o 1204 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp516 1205 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp520 1206 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theorem3anassrs 1207 Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)

Theorem3adant1l 1208 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant1r 1209 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2l 1210 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2r 1211 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3l 1212 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3r 1213 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theoremsyl12anc 1214 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl21anc 1215 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl3anc 1216 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl22anc 1217 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl13anc 1218 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl31anc 1219 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl112anc 1220 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl121anc 1221 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl211anc 1222 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl23anc 1223 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl32anc 1224 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl122anc 1225 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl212anc 1226 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl221anc 1227 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl113anc 1228 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl131anc 1229 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl311anc 1230 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl33anc 1231 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl222anc 1232 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl123anc 1233 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl132anc 1234 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl213anc 1235 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl231anc 1236 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl312anc 1237 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl321anc 1238 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

Theoremsyl133anc 1239 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl313anc 1240 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl331anc 1241 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl223anc 1242 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl232anc 1243 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl322anc 1244 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl233anc 1245 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl323anc 1246 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl332anc 1247 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl333anc 1248 A syllogism inference combined with contraction. (Contributed by NM, 10-Mar-2012.)

Theoremsyl3an1 1249 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2 1250 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3 1251 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an1b 1252 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2b 1253 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3b 1254 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an1br 1255 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an2br 1256 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an3br 1257 A syllogism inference. (Contributed by NM, 22-Aug-1995.)

Theoremsyl3an 1258 A triple syllogism inference. (Contributed by NM, 13-May-2004.)

Theoremsyl3anb 1259 A triple syllogism inference. (Contributed by NM, 15-Oct-2005.)

Theoremsyl3anbr 1260 A triple syllogism inference. (Contributed by NM, 29-Dec-2011.)

Theoremsyld3an3 1261 A syllogism inference. (Contributed by NM, 20-May-2007.)

Theoremsyld3an1 1262 A syllogism inference. (Contributed by NM, 7-Jul-2008.)

Theoremsyld3an2 1263 A syllogism inference. (Contributed by NM, 20-May-2007.)

Theoremsyl3anl1 1264 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl2 1265 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl3 1266 A syllogism inference. (Contributed by NM, 24-Feb-2005.)

Theoremsyl3anl 1267 A triple syllogism inference. (Contributed by NM, 24-Dec-2006.)

Theoremsyl3anr1 1268 A syllogism inference. (Contributed by NM, 31-Jul-2007.)

Theoremsyl3anr2 1269 A syllogism inference. (Contributed by NM, 1-Aug-2007.)

Theoremsyl3anr3 1270 A syllogism inference. (Contributed by NM, 23-Aug-2007.)

Theorem3impdi 1271 Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)

Theorem3impdir 1272 Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.)

Theorem3anidm12 1273 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)

Theorem3anidm13 1274 Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)

Theorem3anidm23 1275 Inference from idempotent law for conjunction. (Contributed by NM, 1-Feb-2007.)

Theoremsyl2an3an 1276 syl3an 1258 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.)

Theoremsyl2an23an 1277 Deduction related to syl3an 1258 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.)

Theorem3ori 1278 Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)

Theorem3jao 1279 Disjunction of 3 antecedents. (Contributed by NM, 8-Apr-1994.)

Theorem3jaob 1280 Disjunction of 3 antecedents. (Contributed by NM, 13-Sep-2011.)

Theorem3jaoi 1281 Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)

Theorem3jaod 1282 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)

Theorem3jaoian 1283 Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)

Theorem3jaodan 1284 Disjunction of 3 antecedents (deduction). (Contributed by NM, 14-Oct-2005.)

Theoremmpjao3dan 1285 Eliminate a 3-way disjunction in a deduction. (Contributed by Thierry Arnoux, 13-Apr-2018.)

Theorem3jaao 1286 Inference conjoining and disjoining the antecedents of three implications. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Theorem3ianorr 1287 Triple disjunction implies negated triple conjunction. (Contributed by Jim Kingdon, 23-Dec-2018.)

Theoremsyl3an9b 1288 Nested syllogism inference conjoining 3 dissimilar antecedents. (Contributed by NM, 1-May-1995.)

Theorem3orbi123d 1289 Deduction joining 3 equivalences to form equivalence of disjunctions. (Contributed by NM, 20-Apr-1994.)

Theorem3anbi123d 1290 Deduction joining 3 equivalences to form equivalence of conjunctions. (Contributed by NM, 22-Apr-1994.)

Theorem3anbi12d 1291 Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi13d 1292 Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi23d 1293 Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi1d 1294 Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi2d 1295 Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi3d 1296 Deduction adding conjuncts to an equivalence. (Contributed by NM, 8-Sep-2006.)

Theorem3anim123d 1297 Deduction joining 3 implications to form implication of conjunctions. (Contributed by NM, 24-Feb-2005.)

Theorem3orim123d 1298 Deduction joining 3 implications to form implication of disjunctions. (Contributed by NM, 4-Apr-1997.)

Theoreman6 1299 Rearrangement of 6 conjuncts. (Contributed by NM, 13-Mar-1995.)

Theorem3an6 1300 Analog of an4 575 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)

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