Theorem simp211 1307

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 1199	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1130	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  cdleme27a  37505  cdlemk5u  37999  cdlemk6u  38000  cdlemk7u  38008  cdlemk11u  38009  cdlemk12u  38010  cdlemk7u-2N  38026  cdlemk11u-2N  38027  cdlemk12u-2N  38028  cdlemk20-2N  38030  cdlemk22  38031  cdlemk33N  38047  cdlemk53b  38094  cdlemk53  38095  cdlemk55a  38097  cdlemkyyN  38100  cdlemk43N  38101