Theorem simp212 1309

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

Assertion

Ref	Expression
simp212	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Proof of Theorem simp212

Step	Hyp	Ref	Expression
1		simp12 1201	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1131	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1084

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 206  df-an 395  df-3an 1086

This theorem is referenced by:  cdleme27a  40066  cdlemk5u  40560  cdlemk6u  40561  cdlemk7u  40569  cdlemk11u  40570  cdlemk12u  40571  cdlemk7u-2N  40587  cdlemk11u-2N  40588  cdlemk12u-2N  40589  cdlemk20-2N  40591  cdlemk22  40592  cdlemk22-3  40600  cdlemk33N  40608  cdlemk53b  40655  cdlemk53  40656  cdlemk55a  40658  cdlemkyyN  40661  cdlemk43N  40662