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  40707  dalempnes  40708  dalemrot  40714  dath2  40794  cdleme18d  41352  cdleme20i  41374  cdleme20j  41375  cdleme20l2  41378  cdleme20l  41379  cdleme20m  41380  cdleme20  41381  cdleme21j  41393  cdleme22eALTN  41402  cdlemk16a  41913  cdlemk12u-2N  41947  cdlemk21-2N  41948  cdlemk22  41950  cdlemk31  41953  cdlemk32  41954  cdlemk11ta  41986  cdlemk11tc  42002