Theorem simp312 1322

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 1205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  dalemrot  39829  dalem-cly  39843  dath2  39909  cdleme26e  40531  cdleme38m  40635  cdleme38n  40636  cdleme39n  40638  cdlemg28b  40875  cdlemk7  41020  cdlemk11  41021  cdlemk12  41022  cdlemk7u  41042  cdlemk11u  41043  cdlemk12u  41044  cdlemk22  41065  cdlemk23-3  41074  cdlemk25-3  41076