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

Theoremsimplr1 1101 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜑)

Theoremsimplr2 1102 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜓)

Theoremsimplr3 1103 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)

Theoremsimprl1 1104 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Theoremsimprl2 1105 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Theoremsimprl3 1106 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Theoremsimprr1 1107 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Theoremsimprr2 1108 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Theoremsimprr3 1109 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Theoremsimpl1l 1110 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏) → 𝜑)

Theoremsimpl1r 1111 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏) → 𝜓)

Theoremsimpl2l 1112 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒 ∧ (𝜑𝜓) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Theoremsimpl2r 1113 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒 ∧ (𝜑𝜓) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theoremsimpl3l 1114 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)

Theoremsimpl3r 1115 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜓)

Theoremsimpr1l 1116 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)

Theoremsimpr1r 1117 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)

Theoremsimpr2l 1118 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃)) → 𝜑)

Theoremsimpr2r 1119 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃)) → 𝜓)

Theoremsimpr3l 1120 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜑)

Theoremsimpr3r 1121 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Theoremsimp1ll 1122 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃𝜏) → 𝜑)

Theoremsimp1lr 1123 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃𝜏) → 𝜓)

Theoremsimp1rl 1124 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒 ∧ (𝜑𝜓)) ∧ 𝜃𝜏) → 𝜑)

Theoremsimp1rr 1125 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒 ∧ (𝜑𝜓)) ∧ 𝜃𝜏) → 𝜓)

Theoremsimp2ll 1126 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃 ∧ ((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜑)

Theoremsimp2lr 1127 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃 ∧ ((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Theoremsimp2rl 1128 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃 ∧ (𝜒 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)

Theoremsimp2rr 1129 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃 ∧ (𝜒 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜓)

Theoremsimp3ll 1130 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃𝜏 ∧ ((𝜑𝜓) ∧ 𝜒)) → 𝜑)

Theoremsimp3lr 1131 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃𝜏 ∧ ((𝜑𝜓) ∧ 𝜒)) → 𝜓)

Theoremsimp3rl 1132 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)

Theoremsimp3rr 1133 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜓)

Theoremsimpl11 1134 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂) → 𝜑)

Theoremsimpl12 1135 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂) → 𝜓)

Theoremsimpl13 1136 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂) → 𝜒)

Theoremsimpl21 1137 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜑)

Theoremsimpl22 1138 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜓)

Theoremsimpl23 1139 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Theoremsimpl31 1140 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜑)

Theoremsimpl32 1141 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜓)

Theoremsimpl33 1142 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)

Theoremsimpr11 1143 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜑)

Theoremsimpr12 1144 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)

Theoremsimpr13 1145 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜒)

Theoremsimpr21 1146 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)

Theoremsimpr22 1147 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)

Theoremsimpr23 1148 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜒)

Theoremsimpr31 1149 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)

Theoremsimpr32 1150 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜓)

Theoremsimpr33 1151 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)

Theoremsimp1l1 1152 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜑)

Theoremsimp1l2 1153 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜓)

Theoremsimp1l3 1154 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜒)

Theoremsimp1r1 1155 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜑)

Theoremsimp1r2 1156 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜓)

Theoremsimp1r3 1157 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏𝜂) → 𝜒)

Theoremsimp2l1 1158 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Theoremsimp2l2 1159 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)

Theoremsimp2l3 1160 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

Theoremsimp2r1 1161 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜑)

Theoremsimp2r2 1162 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜓)

Theoremsimp2r3 1163 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)

Theoremsimp3l1 1164 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Theoremsimp3l2 1165 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Theoremsimp3l3 1166 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Theoremsimp3r1 1167 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Theoremsimp3r2 1168 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Theoremsimp3r3 1169 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Theoremsimp11l 1170 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏𝜂) → 𝜑)

Theoremsimp11r 1171 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜏𝜂) → 𝜓)

Theoremsimp12l 1172 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒 ∧ (𝜑𝜓) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜑)

Theoremsimp12r 1173 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒 ∧ (𝜑𝜓) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜓)

Theoremsimp13l 1174 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏𝜂) → 𝜑)

Theoremsimp13r 1175 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏𝜂) → 𝜓)

Theoremsimp21l 1176 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜂) → 𝜑)

Theoremsimp21r 1177 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ ((𝜑𝜓) ∧ 𝜒𝜃) ∧ 𝜂) → 𝜓)

Theoremsimp22l 1178 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Theoremsimp22r 1179 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃) ∧ 𝜂) → 𝜓)

Theoremsimp23l 1180 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜂) → 𝜑)

Theoremsimp23r 1181 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜂) → 𝜓)

Theoremsimp31l 1182 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜑)

Theoremsimp31r 1183 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ ((𝜑𝜓) ∧ 𝜒𝜃)) → 𝜓)

Theoremsimp32l 1184 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃)) → 𝜑)

Theoremsimp32r 1185 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜒 ∧ (𝜑𝜓) ∧ 𝜃)) → 𝜓)

Theoremsimp33l 1186 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜑)

Theoremsimp33r 1187 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Theoremsimp111 1188 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)

Theoremsimp112 1189 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜓)

Theoremsimp113 1190 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)

Theoremsimp121 1191 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜂𝜁) → 𝜑)

Theoremsimp122 1192 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜂𝜁) → 𝜓)

Theoremsimp123 1193 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜂𝜁) → 𝜒)

Theoremsimp131 1194 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜑)

Theoremsimp132 1195 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜓)

Theoremsimp133 1196 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
(((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜒)

Theoremsimp211 1197 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜑)

Theoremsimp212 1198 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)

Theoremsimp213 1199 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)

Theoremsimp221 1200 Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
((𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜑)

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268 26701-26800 269 26801-26900 270 26901-27000 271 27001-27100 272 27101-27200 273 27201-27300 274 27301-27400 275 27401-27500 276 27501-27600 277 27601-27700 278 27701-27800 279 27801-27900 280 27901-28000 281 28001-28100 282 28101-28200 283 28201-28300 284 28301-28400 285 28401-28500 286 28501-28600 287 28601-28700 288 28701-28800 289 28801-28900 290 28901-29000 291 29001-29100 292 29101-29200 293 29201-29300 294 29301-29400 295 29401-29500 296 29501-29600 297 29601-29700 298 29701-29800 299 29801-29900 300 29901-30000 301 30001-30100 302 30101-30200 303 30201-30300 304 30301-30400 305 30401-30500 306 30501-30600 307 30601-30700 308 30701-30800 309 30801-30900 310 30901-31000 311 31001-31100 312 31101-31200 313 31201-31300 314 31301-31400 315 31401-31500 316 31501-31600 317 31601-31700 318 31701-31800 319 31801-31900 320 31901-32000 321 32001-32100 322 32101-32200 323 32201-32300 324 32301-32400 325 32401-32500 326 32501-32600 327 32601-32700 328 32701-32800 329 32801-32900 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