Theorem simp212 1314

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 1206	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1135	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  cdleme27a  40827  cdlemk5u  41321  cdlemk6u  41322  cdlemk7u  41330  cdlemk11u  41331  cdlemk12u  41332  cdlemk7u-2N  41348  cdlemk11u-2N  41349  cdlemk12u-2N  41350  cdlemk20-2N  41352  cdlemk22  41353  cdlemk22-3  41361  cdlemk33N  41369  cdlemk53b  41416  cdlemk53  41417  cdlemk55a  41419  cdlemkyyN  41422  cdlemk43N  41423