Theorem simp212 1368

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 1218	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1125	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1071

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 199  df-an 387  df-3an 1073

This theorem is referenced by:  cdleme27a  36521  cdlemk5u  37015  cdlemk6u  37016  cdlemk7u  37024  cdlemk11u  37025  cdlemk12u  37026  cdlemk7u-2N  37042  cdlemk11u-2N  37043  cdlemk12u-2N  37044  cdlemk20-2N  37046  cdlemk22  37047  cdlemk22-3  37055  cdlemk33N  37063  cdlemk53b  37110  cdlemk53  37111  cdlemk55a  37113  cdlemkyyN  37116  cdlemk43N  37117