Theorem simp321 1324

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp321	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simp321

Step	Hyp	Ref	Expression
1		simp21 1207	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  dalemcnes  39637  dalempnes  39638  dalemrot  39644  dath2  39724  cdleme18d  40282  cdleme20i  40304  cdleme20j  40305  cdleme20l2  40308  cdleme20l  40309  cdleme20m  40310  cdleme20  40311  cdleme21j  40323  cdleme22eALTN  40332  cdlemk16a  40843  cdlemk12u-2N  40877  cdlemk21-2N  40878  cdlemk22  40880  cdlemk31  40883  cdlemk32  40884  cdlemk11ta  40916  cdlemk11tc  40932