P. 12 of Theorem List - Metamath Proof Explorer

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

Type	Label	Description
Statement
Theorem	simpll2 1101	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ps )
Theorem	simpll3 1102	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ch )
Theorem	simplr1 1103	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ph )
Theorem	simplr2 1104	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ps )
Theorem	simplr3 1105	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta ) -> ch )
Theorem	simprl1 1106	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ph )
Theorem	simprl2 1107	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ps )
Theorem	simprl3 1108	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ch )
Theorem	simprr1 1109	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simprr2 1110	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simprr3 1111	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	simpl1l 1112	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch /\ th ) /\ ta ) -> ph )
Theorem	simpl1r 1113	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch /\ th ) /\ ta ) -> ps )
Theorem	simpl2l 1114	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta ) -> ph )
Theorem	simpl2r 1115	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta ) -> ps )
Theorem	simpl3l 1116	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta ) -> ph )
Theorem	simpl3r 1117	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta ) -> ps )
Theorem	simpr1l 1118	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ph )
Theorem	simpr1r 1119	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )
Theorem	simpr2l 1120	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ph )
Theorem	simpr2r 1121	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ps )
Theorem	simpr3l 1122	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ph )
Theorem	simpr3r 1123	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ps )
Theorem	simp1ll 1124	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th /\ ta ) -> ph )
Theorem	simp1lr 1125	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th /\ ta ) -> ps )
Theorem	simp1rl 1126	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) ) /\ th /\ ta ) -> ph )
Theorem	simp1rr 1127	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) ) /\ th /\ ta ) -> ps )
Theorem	simp2ll 1128	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ( ph /\ ps ) /\ ch ) /\ ta ) -> ph )
Theorem	simp2lr 1129	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ( ph /\ ps ) /\ ch ) /\ ta ) -> ps )
Theorem	simp2rl 1130	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ch /\ ( ph /\ ps ) ) /\ ta ) -> ph )
Theorem	simp2rr 1131	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ( ch /\ ( ph /\ ps ) ) /\ ta ) -> ps )
Theorem	simp3ll 1132	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ( ph /\ ps ) /\ ch ) ) -> ph )
Theorem	simp3lr 1133	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ( ph /\ ps ) /\ ch ) ) -> ps )
Theorem	simp3rl 1134	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ch /\ ( ph /\ ps ) ) ) -> ph )
Theorem	simp3rr 1135	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( th /\ ta /\ ( ch /\ ( ph /\ ps ) ) ) -> ps )
Theorem	simpl11 1136	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ph )
Theorem	simpl12 1137	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ps )
Theorem	simpl13 1138	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et ) -> ch )
Theorem	simpl21 1139	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ph )
Theorem	simpl22 1140	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ps )
Theorem	simpl23 1141	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et ) -> ch )
Theorem	simpl31 1142	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ph )
Theorem	simpl32 1143	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ps )
Theorem	simpl33 1144	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ch )
Theorem	simpr11 1145	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )
Theorem	simpr12 1146	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ps )
Theorem	simpr13 1147	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ch )
Theorem	simpr21 1148	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ph )
Theorem	simpr22 1149	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ps )
Theorem	simpr23 1150	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ( ph /\ ps /\ ch ) /\ ta ) ) -> ch )
Theorem	simpr31 1151	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simpr32 1152	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simpr33 1153	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	simp1l1 1154	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta /\ et ) -> ph )
Theorem	simp1l2 1155	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta /\ et ) -> ps )
Theorem	simp1l3 1156	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta /\ et ) -> ch )
Theorem	simp1r1 1157	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ph )
Theorem	simp1r2 1158	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ps )
Theorem	simp1r3 1159	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) ) /\ ta /\ et ) -> ch )
Theorem	simp2l1 1160	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ph )
Theorem	simp2l2 1161	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ps )
Theorem	simp2l3 1162	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps /\ ch ) /\ th ) /\ et ) -> ch )
Theorem	simp2r1 1163	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ph )
Theorem	simp2r2 1164	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ps )
Theorem	simp2r3 1165	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( th /\ ( ph /\ ps /\ ch ) ) /\ et ) -> ch )
Theorem	simp3l1 1166	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ph )
Theorem	simp3l2 1167	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ps )
Theorem	simp3l3 1168	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps /\ ch ) /\ th ) ) -> ch )
Theorem	simp3r1 1169	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ph )
Theorem	simp3r2 1170	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )
Theorem	simp3r3 1171	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ch )
Theorem	simp11l 1172	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch /\ th ) /\ ta /\ et ) -> ph )
Theorem	simp11r 1173	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps ) /\ ch /\ th ) /\ ta /\ et ) -> ps )
Theorem	simp12l 1174	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta /\ et ) -> ph )
Theorem	simp12r 1175	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ ( ph /\ ps ) /\ th ) /\ ta /\ et ) -> ps )
Theorem	simp13l 1176	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta /\ et ) -> ph )
Theorem	simp13r 1177	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta /\ et ) -> ps )
Theorem	simp21l 1178	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) /\ et ) -> ph )
Theorem	simp21r 1179	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ( ph /\ ps ) /\ ch /\ th ) /\ et ) -> ps )
Theorem	simp22l 1180	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) /\ et ) -> ph )
Theorem	simp22r 1181	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ ( ph /\ ps ) /\ th ) /\ et ) -> ps )
Theorem	simp23l 1182	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) /\ et ) -> ph )
Theorem	simp23r 1183	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ ( ch /\ th /\ ( ph /\ ps ) ) /\ et ) -> ps )
Theorem	simp31l 1184	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ph )
Theorem	simp31r 1185	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ( ph /\ ps ) /\ ch /\ th ) ) -> ps )
Theorem	simp32l 1186	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ph )
Theorem	simp32r 1187	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ ( ph /\ ps ) /\ th ) ) -> ps )
Theorem	simp33l 1188	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ph )
Theorem	simp33r 1189	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ta /\ et /\ ( ch /\ th /\ ( ph /\ ps ) ) ) -> ps )
Theorem	simp111 1190	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ph )
Theorem	simp112 1191	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ps )
Theorem	simp113 1192	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ch )
Theorem	simp121 1193	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ph )
Theorem	simp122 1194	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ps )
Theorem	simp123 1195	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ch )
Theorem	simp131 1196	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ph )
Theorem	simp132 1197	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ps )
Theorem	simp133 1198	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ch )
Theorem	simp211 1199	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ph )
Theorem	simp212 1200	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ ze ) -> ps )