Theorem simp213 1418

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

Assertion

Ref	Expression
simp213	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp213

Step	Hyp	Ref	Expression
1		simp13 1268	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant2 1170	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1113

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 1115

This theorem is referenced by:  cdleme27a  36443  cdlemk5u  36937  cdlemk6u  36938  cdlemk7u  36946  cdlemk11u  36947  cdlemk12u  36948  cdlemk7u-2N  36964  cdlemk11u-2N  36965  cdlemk12u-2N  36966  cdlemk20-2N  36968  cdlemk22  36969  cdlemk22-3  36977  cdlemk33N  36985  cdlemk53b  37032  cdlemk53  37033  cdlemk55a  37035  cdlemkyyN  37038  cdlemk43N  37039