Theorem simp211 1414

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

Assertion

Ref	Expression
simp211	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp211

Step	Hyp	Ref	Expression
1		simp11 1264	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1168	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1111

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 1113

This theorem is referenced by:  cdleme27a  36437  cdlemk5u  36931  cdlemk6u  36932  cdlemk7u  36940  cdlemk11u  36941  cdlemk12u  36942  cdlemk7u-2N  36958  cdlemk11u-2N  36959  cdlemk12u-2N  36960  cdlemk20-2N  36962  cdlemk22  36963  cdlemk33N  36979  cdlemk53b  37026  cdlemk53  37027  cdlemk55a  37029  cdlemkyyN  37032  cdlemk43N  37033