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  40332  cdlemk5u  40826  cdlemk6u  40827  cdlemk7u  40835  cdlemk11u  40836  cdlemk12u  40837  cdlemk7u-2N  40853  cdlemk11u-2N  40854  cdlemk12u-2N  40855  cdlemk20-2N  40857  cdlemk22  40858  cdlemk22-3  40866  cdlemk33N  40874  cdlemk53b  40921  cdlemk53  40922  cdlemk55a  40924  cdlemkyyN  40927  cdlemk43N  40928