Theorem simp312 1340

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

Assertion

Ref	Expression
simp312	⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓)

Proof of Theorem simp312

Step	Hyp	Ref	Expression
1		simp12 1223	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 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:  dalemrot  40821  dalem-cly  40835  dath2  40901  cdleme26e  41523  cdleme38m  41627  cdleme38n  41628  cdleme39n  41630  cdlemg28b  41867  cdlemk7  42012  cdlemk11  42013  cdlemk12  42014  cdlemk7u  42034  cdlemk11u  42035  cdlemk12u  42036  cdlemk22  42057  cdlemk23-3  42066  cdlemk25-3  42068