Theorem simp322 1343

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 1226	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

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:  dalemqnet  40846  dalemrot  40851  dath2  40931  cdleme18d  41489  cdleme20i  41511  cdleme20j  41512  cdleme20l2  41515  cdleme20l  41516  cdleme20m  41517  cdleme20  41518  cdleme21j  41530  cdleme22eALTN  41539  cdleme26eALTN  41555  cdlemk16a  42050  cdlemk12u-2N  42084  cdlemk21-2N  42085  cdlemk22  42087  cdlemk31  42090  cdlemk32  42091  cdlemk11ta  42123  cdlemk11tc  42139