Theorem simp212 1310

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 1202	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1132	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1085

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 1087

This theorem is referenced by:  cdleme27a  39541  cdlemk5u  40035  cdlemk6u  40036  cdlemk7u  40044  cdlemk11u  40045  cdlemk12u  40046  cdlemk7u-2N  40062  cdlemk11u-2N  40063  cdlemk12u-2N  40064  cdlemk20-2N  40066  cdlemk22  40067  cdlemk22-3  40075  cdlemk33N  40083  cdlemk53b  40130  cdlemk53  40131  cdlemk55a  40133  cdlemkyyN  40136  cdlemk43N  40137