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)

Syntax hints:   → wi 4   ∧ w3a 1103

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 210  df-an 401  df-3an 1105

This theorem is referenced by:  dalemcnes  40444  dalempnes  40445  dalemrot  40451  dath2  40531  cdleme18d  41089  cdleme20i  41111  cdleme20j  41112  cdleme20l2  41115  cdleme20l  41116  cdleme20m  41117  cdleme20  41118  cdleme21j  41130  cdleme22eALTN  41139  cdlemk16a  41650  cdlemk12u-2N  41684  cdlemk21-2N  41685  cdlemk22  41687  cdlemk31  41690  cdlemk32  41691  cdlemk11ta  41723  cdlemk11tc  41739