Theorem simp321 1204

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 1087	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant3 1077	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1031

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 196  df-an 385  df-3an 1033

This theorem is referenced by:  dalemcnes  33748  dalempnes  33749  dalemrot  33755  dath2  33835  cdleme18d  34394  cdleme20i  34417  cdleme20j  34418  cdleme20l2  34421  cdleme20l  34422  cdleme20m  34423  cdleme20  34424  cdleme21j  34436  cdleme22eALTN  34445  cdlemk16a  34956  cdlemk12u-2N  34990  cdlemk21-2N  34991  cdlemk22  34993  cdlemk31  34996  cdlemk32  34997  cdlemk11ta  35029  cdlemk11tc  35045