Theorem simp321 1342

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 1225	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1153	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  dalemcnes  40524  dalempnes  40525  dalemrot  40531  dath2  40611  cdleme18d  41169  cdleme20i  41191  cdleme20j  41192  cdleme20l2  41195  cdleme20l  41196  cdleme20m  41197  cdleme20  41198  cdleme21j  41210  cdleme22eALTN  41219  cdlemk16a  41730  cdlemk12u-2N  41764  cdlemk21-2N  41765  cdlemk22  41767  cdlemk31  41770  cdlemk32  41771  cdlemk11ta  41803  cdlemk11tc  41819