Theorem simp322 1338

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp322	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322

Step	Hyp	Ref	Expression
1		simp22 1221	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1148	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1098

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 209  df-an 400  df-3an 1100

This theorem is referenced by:  dalemqnet  40276  dalemrot  40281  dath2  40361  cdleme18d  40919  cdleme20i  40941  cdleme20j  40942  cdleme20l2  40945  cdleme20l  40946  cdleme20m  40947  cdleme20  40948  cdleme21j  40960  cdleme22eALTN  40969  cdleme26eALTN  40985  cdlemk16a  41480  cdlemk12u-2N  41514  cdlemk21-2N  41515  cdlemk22  41517  cdlemk31  41520  cdlemk32  41521  cdlemk11ta  41553  cdlemk11tc  41569