Theorem simp211 1311

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 1203	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1134	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1087

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 397  df-3an 1089

This theorem is referenced by:  cdleme27a  39043  cdlemk5u  39537  cdlemk6u  39538  cdlemk7u  39546  cdlemk11u  39547  cdlemk12u  39548  cdlemk7u-2N  39564  cdlemk11u-2N  39565  cdlemk12u-2N  39566  cdlemk20-2N  39568  cdlemk22  39569  cdlemk33N  39585  cdlemk53b  39632  cdlemk53  39633  cdlemk55a  39635  cdlemkyyN  39638  cdlemk43N  39639