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Theorem List for New Foundations Explorer - 1101-1200   *Has distinct variable group(s)
TypeLabelDescription
Statement

Theoremsimp233 1101 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp311 1102 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp312 1103 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp313 1104 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp321 1105 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp322 1106 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp323 1107 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp331 1108 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp332 1109 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp333 1110 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theorem3adantl1 1111 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Theorem3adantl2 1112 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Theorem3adantl3 1113 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Theorem3adantr1 1114 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Theorem3adantr2 1115 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Theorem3adantr3 1116 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Theorem3anibar 1123 Remove a hypothesis from the second member of a biimplication. (Contributed by FL, 22-Jul-2008.)

Theorem3mix1 1124 Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Theorem3mix2 1125 Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Theorem3mix3 1126 Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Theorem3mix1i 1127 Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Theorem3mix2i 1128 Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Theorem3mix3i 1129 Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Theorem3pm3.2i 1130 Infer conjunction of premises. (Contributed by NM, 10-Feb-1995.)

Theorempm3.2an3 1131 pm3.2 434 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)

Theorem3jca 1132 Join consequents with conjunction. (Contributed by NM, 9-Apr-1994.)

Theorem3jcad 1133 Deduction conjoining the consequents of three implications. (Contributed by NM, 25-Sep-2005.)

Theoremmpbir3an 1134 Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011.)

Theoremmpbir3and 1135 Detach a conjunction of truths in a biconditional. (Contributed by Mario Carneiro, 11-May-2014.) (Revised by Mario Carneiro, 9-Jan-2015.)

Theoremsyl3anbrc 1136 Syllogism inference. (Contributed by Mario Carneiro, 11-May-2014.)

Theorem3anim123i 1137 Join antecedents and consequents with conjunction. (Contributed by NM, 8-Apr-1994.)

Theorem3anim1i 1138 Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)

Theorem3anim3i 1139 Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)

Theorem3anbi123i 1140 Join 3 biconditionals with conjunction. (Contributed by NM, 21-Apr-1994.)

Theorem3orbi123i 1141 Join 3 biconditionals with disjunction. (Contributed by NM, 17-May-1994.)

Theorem3anbi1i 1142 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi2i 1143 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi3i 1144 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3imp 1145 Importation inference. (Contributed by NM, 8-Apr-1994.)

Theorem3impa 1146 Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3impb 1147 Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3impia 1148 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3impib 1149 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3exp 1150 Exportation inference. (Contributed by NM, 30-May-1994.)

Theorem3expa 1151 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expb 1152 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expia 1153 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3expib 1154 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3com12 1155 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Theorem3com13 1156 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3com23 1157 Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3coml 1158 Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996.)

Theorem3comr 1159 Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)

Theorem3adant3r1 1160 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)

Theorem3adant3r2 1161 Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)

Theorem3adant3r3 1162 Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)

Theorem3an1rs 1163 Swap conjuncts. (Contributed by NM, 16-Dec-2007.)

Theorem3imp1 1164 Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3impd 1165 Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3imp2 1166 Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp1 1167 Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3expd 1168 Exportation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theorem3exp2 1169 Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Theoremexp5o 1170 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp516 1171 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theoremexp520 1172 A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Theorem3anassrs 1173 Associative law for conjunction applied to antecedent (eliminates syllogism). (Contributed by Mario Carneiro, 4-Jan-2017.)

Theorem3adant1l 1174 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant1r 1175 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2l 1176 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant2r 1177 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3l 1178 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theorem3adant3r 1179 Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Theoremsyl12anc 1180 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl21anc 1181 Syllogism combined with contraction. (Contributed by Jeff Hankins, 1-Aug-2009.)

Theoremsyl3anc 1182 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl22anc 1183 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl13anc 1184 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl31anc 1185 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl112anc 1186 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl121anc 1187 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl211anc 1188 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl23anc 1189 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl32anc 1190 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl122anc 1191 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl212anc 1192 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl221anc 1193 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl113anc 1194 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl131anc 1195 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl311anc 1196 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl33anc 1197 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl222anc 1198 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl123anc 1199 Syllogism combined with contraction. (Contributed by NM, 11-Mar-2012.)

Theoremsyl132anc 1200 Syllogism combined with contraction. (Contributed by NM, 11-Jul-2012.)

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