Theorem simp212 1311

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 1203	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1133	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  cdleme27a  38593  cdlemk5u  39087  cdlemk6u  39088  cdlemk7u  39096  cdlemk11u  39097  cdlemk12u  39098  cdlemk7u-2N  39114  cdlemk11u-2N  39115  cdlemk12u-2N  39116  cdlemk20-2N  39118  cdlemk22  39119  cdlemk22-3  39127  cdlemk33N  39135  cdlemk53b  39182  cdlemk53  39183  cdlemk55a  39185  cdlemkyyN  39188  cdlemk43N  39189