Theorem simp212 1311

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 1203	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1133	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 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:  cdleme27a  40349  cdlemk5u  40843  cdlemk6u  40844  cdlemk7u  40852  cdlemk11u  40853  cdlemk12u  40854  cdlemk7u-2N  40870  cdlemk11u-2N  40871  cdlemk12u-2N  40872  cdlemk20-2N  40874  cdlemk22  40875  cdlemk22-3  40883  cdlemk33N  40891  cdlemk53b  40938  cdlemk53  40939  cdlemk55a  40941  cdlemkyyN  40944  cdlemk43N  40945