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

Theoremsimp22l 1101 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp22r 1102 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp23l 1103 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp23r 1104 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp31l 1105 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp31r 1106 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp32l 1107 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp32r 1108 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp33l 1109 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp33r 1110 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp111 1111 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp112 1112 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp113 1113 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp121 1114 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp122 1115 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp123 1116 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp131 1117 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp132 1118 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp133 1119 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp211 1120 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp212 1121 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp213 1122 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp221 1123 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp222 1124 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp223 1125 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp231 1126 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp232 1127 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp233 1128 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp311 1129 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp312 1130 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp313 1131 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp321 1132 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp322 1133 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp323 1134 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp331 1135 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp332 1136 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theoremsimp333 1137 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Theorem3adantl1 1138 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Theorem3adantl2 1139 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Theorem3adantl3 1140 Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Theorem3adantr1 1141 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Theorem3adantr2 1142 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Theorem3adantr3 1143 Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Theorem3ad2antr1 1147 Deduction adding a conjuncts to antecedent. (Contributed by NM, 25-Dec-2007.)

Theorem3ad2antr2 1148 Deduction adding a conjuncts to antecedent. (Contributed by NM, 27-Dec-2007.)

Theorem3ad2antr3 1149 Deduction adding a conjuncts to antecedent. (Contributed by NM, 30-Dec-2007.)

Theorem3anibar 1150 Remove a hypothesis from the second member of a biimplication. (Contributed by FL, 22-Jul-2008.)

Theorem3mix1 1151 Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Theorem3mix2 1152 Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Theorem3mix3 1153 Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Theorem3mix1i 1154 Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Theorem3mix2i 1155 Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Theorem3mix3i 1156 Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Theorem3mix1d 1157 Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)

Theorem3mix2d 1158 Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)

Theorem3mix3d 1159 Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)

Theorem3pm3.2i 1160 Infer conjunction of premises. (Contributed by NM, 10-Feb-1995.)

Theorempm3.2an3 1161 pm3.2 138 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)

Theorem3jca 1162 Join consequents with conjunction. (Contributed by NM, 9-Apr-1994.)

Theorem3jcad 1163 Deduction conjoining the consequents of three implications. (Contributed by NM, 25-Sep-2005.)

Theoremmpbir3an 1164 Detach a conjunction of truths in a biconditional. (Contributed by NM, 16-Sep-2011.) (Revised by NM, 9-Jan-2015.)

Theoremmpbir3and 1165 Detach a conjunction of truths in a biconditional. (Contributed by Mario Carneiro, 11-May-2014.)

Theoremsyl3anbrc 1166 Syllogism inference. (Contributed by Mario Carneiro, 11-May-2014.)

Theorem3anim123i 1167 Join antecedents and consequents with conjunction. (Contributed by NM, 8-Apr-1994.)

Theorem3anim1i 1168 Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)

Theorem3anim2i 1169 Add two conjuncts to antecedent and consequent. (Contributed by AV, 21-Nov-2019.)

Theorem3anim3i 1170 Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)

Theorem3anbi123i 1171 Join 3 biconditionals with conjunction. (Contributed by NM, 21-Apr-1994.)

Theorem3orbi123i 1172 Join 3 biconditionals with disjunction. (Contributed by NM, 17-May-1994.)

Theorem3anbi1i 1173 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi2i 1174 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3anbi3i 1175 Inference adding two conjuncts to each side of a biconditional. (Contributed by NM, 8-Sep-2006.)

Theorem3imp 1176 Importation inference. (Contributed by NM, 8-Apr-1994.)

Theorem3impa 1177 Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3impb 1178 Importation from double to triple conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3impia 1179 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3impib 1180 Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Theorem3exp 1181 Exportation inference. (Contributed by NM, 30-May-1994.)

Theorem3expa 1182 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expb 1183 Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Theorem3expia 1184 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3expib 1185 Exportation from triple conjunction. (Contributed by NM, 19-May-2007.)

Theorem3com12 1186 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Theorem3com13 1187 Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3com23 1188 Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)

Theorem3coml 1189 Commutation in antecedent. Rotate left. (Contributed by NM, 28-Jan-1996.)

Theorem3comr 1190 Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)

Theorem3adant3r1 1191 Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)

Theorem3adant3r2 1192 Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)

Theorem3adant3r3 1193 Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)

Theoremad4ant123 1194 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Theoremad4ant124 1195 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Theoremad4ant134 1196 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Theoremad4ant234 1197 Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Theorem3an1rs 1198 Swap conjuncts. (Contributed by NM, 16-Dec-2007.)

Theorem3imp1 1199 Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)

Theorem3impd 1200 Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)

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