Theorem simp212 1313

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 1205	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1134	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 207  df-an 396  df-3an 1088

This theorem is referenced by:  cdleme27a  40539  cdlemk5u  41033  cdlemk6u  41034  cdlemk7u  41042  cdlemk11u  41043  cdlemk12u  41044  cdlemk7u-2N  41060  cdlemk11u-2N  41061  cdlemk12u-2N  41062  cdlemk20-2N  41064  cdlemk22  41065  cdlemk22-3  41073  cdlemk33N  41081  cdlemk53b  41128  cdlemk53  41129  cdlemk55a  41131  cdlemkyyN  41134  cdlemk43N  41135