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  40975  dalemrot  40980  dath2  41060  cdleme18d  41618  cdleme20i  41640  cdleme20j  41641  cdleme20l2  41644  cdleme20l  41645  cdleme20m  41646  cdleme20  41647  cdleme21j  41659  cdleme22eALTN  41668  cdleme26eALTN  41684  cdlemk16a  42179  cdlemk12u-2N  42213  cdlemk21-2N  42214  cdlemk22  42216  cdlemk31  42219  cdlemk32  42220  cdlemk11ta  42252  cdlemk11tc  42268