P. 13 of Theorem List - Metamath Proof Explorer

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**Theorem List for Metamath Proof Explorer -** 1201-1300 *Has distinct variable group(s)
Type	Label	Description
Statement

Theorem	simp2r 1201	Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒)

Theorem	simp3l 1202	Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜒)

Theorem	simp3r 1203	Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜃)

Theorem	simp11 1204	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Theorem	simp12 1205	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Theorem	simp13 1206	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)

Theorem	simp21 1207	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theorem	simp22 1208	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜒)

Theorem	simp23 1209	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜃)

Theorem	simp31 1210	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜒)

Theorem	simp32 1211	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜃)

Theorem	simp33 1212	Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)
⊢ ((𝜑 ∧ 𝜓 ∧ (𝜒 ∧ 𝜃 ∧ 𝜏)) → 𝜏)

Theorem	simpll1 1213	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Theorem	simpll2 1214	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theorem	simpll3 1215	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜒)

Theorem	simplr1 1216	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜑)

Theorem	simplr2 1217	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜓)

Theorem	simplr3 1218	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏) → 𝜒)

Theorem	simprl1 1219	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Theorem	simprl2 1220	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Theorem	simprl3 1221	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Theorem	simprr1 1222	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Theorem	simprr2 1223	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Theorem	simprr3 1224	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Theorem	simpl1l 1225	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜑)

Theorem	simpl1r 1226	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theorem	simpl2l 1227	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Theorem	simpl2r 1228	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) → 𝜓)

Theorem	simpl3l 1229	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜑)

Theorem	simpl3r 1230	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜓)

Theorem	simpr1l 1231	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Theorem	simpr1r 1232	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Theorem	simpr2l 1233	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Theorem	simpr2r 1234	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

Theorem	simpr3l 1235	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Theorem	simpr3r 1236	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Theorem	simp1ll 1237	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Theorem	simp1lr 1238	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Theorem	simp1rl 1239	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Theorem	simp1rr 1240	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Theorem	simp2ll 1241	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜑)

Theorem	simp2lr 1242	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Theorem	simp2rl 1243	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜑)

Theorem	simp2rr 1244	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜓)

Theorem	simp3ll 1245	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜑)

Theorem	simp3lr 1246	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜓)

Theorem	simp3rl 1247	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Theorem	simp3rr 1248	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜃 ∧ 𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Theorem	simpl11 1249	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂) → 𝜑)

Theorem	simpl12 1250	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂) → 𝜓)

Theorem	simpl13 1251	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜂) → 𝜒)

Theorem	simpl21 1252	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜑)

Theorem	simpl22 1253	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜓)

Theorem	simpl23 1254	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Theorem	simpl31 1255	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜑)

Theorem	simpl32 1256	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜓)

Theorem	simpl33 1257	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒)

Theorem	simpr11 1258	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑)

Theorem	simpr12 1259	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓)

Theorem	simpr13 1260	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒)

Theorem	simpr21 1261	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Theorem	simpr22 1262	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Theorem	simpr23 1263	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜒)

Theorem	simpr31 1264	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Theorem	simpr32 1265	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Theorem	simpr33 1266	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
⊢ ((𝜂 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Theorem	simp1l1 1267	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Theorem	simp1l2 1268	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Theorem	simp1l3 1269	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Theorem	simp1r1 1270	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Theorem	simp1r2 1271	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Theorem	simp1r3 1272	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜒)

Theorem	simp2l1 1273	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Theorem	simp2l2 1274	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)

Theorem	simp2l3 1275	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜒)

Theorem	simp2r1 1276	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜑)

Theorem	simp2r2 1277	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜓)

Theorem	simp2r3 1278	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒)

Theorem	simp3l1 1279	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Theorem	simp3l2 1280	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Theorem	simp3l3 1281	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Theorem	simp3r1 1282	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Theorem	simp3r2 1283	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Theorem	simp3r3 1284	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Theorem	simp11l 1285	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Theorem	simp11r 1286	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Theorem	simp12l 1287	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Theorem	simp12r 1288	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Theorem	simp13l 1289	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏 ∧ 𝜂) → 𝜑)

Theorem	simp13r 1290	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏 ∧ 𝜂) → 𝜓)

Theorem	simp21l 1291	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ∧ 𝜂) → 𝜑)

Theorem	simp21r 1292	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) ∧ 𝜂) → 𝜓)

Theorem	simp22l 1293	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜂) → 𝜑)

Theorem	simp22r 1294	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜂) → 𝜓)

Theorem	simp23l 1295	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜂) → 𝜑)

Theorem	simp23r 1296	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜂) → 𝜓)

Theorem	simp31l 1297	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜑)

Theorem	simp31r 1298	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Theorem	simp32l 1299	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜑)

Theorem	simp32r 1300	Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃)) → 𝜓)

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20501-20600 207 20601-20700 208 20701-20800 209 20801-20900 210 20901-21000 211 21001-21100 212 21101-21200 213 21201-21300 214 21301-21400 215 21401-21500 216 21501-21600 217 21601-21700 218 21701-21800 219 21801-21900 220 21901-22000 221 22001-22100 222 22101-22200 223 22201-22300 224 22301-22400 225 22401-22500 226 22501-22600 227 22601-22700 228 22701-22800 229 22801-22900 230 22901-23000 231 23001-23100 232 23101-23200 233 23201-23300 234 23301-23400 235 23401-23500 236 23501-23600 237 23601-23700 238 23701-23800 239 23801-23900 240 23901-24000 241 24001-24100 242 24101-24200 243 24201-24300 244 24301-24400 245 24401-24500 246 24501-24600 247 24601-24700 248 24701-24800 249 24801-24900 250 24901-25000 251 25001-25100 252 25101-25200 253 25201-25300 254 25301-25400 255 25401-25500 256 25501-25600 257 25601-25700 258 25701-25800 259 25801-25900 260 25901-26000 261 26001-26100 262 26101-26200 263 26201-26300 264 26301-26400 265 26401-26500 266 26501-26600 267 26601-26700 268 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