Theorem simp321 1408

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 1249	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1130	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1072

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 197  df-an 385  df-3an 1074

This theorem is referenced by:  dalemcnes  35457  dalempnes  35458  dalemrot  35464  dath2  35544  cdleme18d  36103  cdleme20i  36125  cdleme20j  36126  cdleme20l2  36129  cdleme20l  36130  cdleme20m  36131  cdleme20  36132  cdleme21j  36144  cdleme22eALTN  36153  cdlemk16a  36664  cdlemk12u-2N  36698  cdlemk21-2N  36699  cdlemk22  36701  cdlemk31  36704  cdlemk32  36705  cdlemk11ta  36737  cdlemk11tc  36753