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  40484  dalemrot  40489  dath2  40569  cdleme18d  41127  cdleme20i  41149  cdleme20j  41150  cdleme20l2  41153  cdleme20l  41154  cdleme20m  41155  cdleme20  41156  cdleme21j  41168  cdleme22eALTN  41177  cdleme26eALTN  41193  cdlemk16a  41688  cdlemk12u-2N  41722  cdlemk21-2N  41723  cdlemk22  41725  cdlemk31  41728  cdlemk32  41729  cdlemk11ta  41761  cdlemk11tc  41777