Theorem simp212 1308

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 1200	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant2 1130	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓)

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  37497  cdlemk5u  37991  cdlemk6u  37992  cdlemk7u  38000  cdlemk11u  38001  cdlemk12u  38002  cdlemk7u-2N  38018  cdlemk11u-2N  38019  cdlemk12u-2N  38020  cdlemk20-2N  38022  cdlemk22  38023  cdlemk22-3  38031  cdlemk33N  38039  cdlemk53b  38086  cdlemk53  38087  cdlemk55a  38089  cdlemkyyN  38092  cdlemk43N  38093