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  40406  cdlemk5u  40900  cdlemk6u  40901  cdlemk7u  40909  cdlemk11u  40910  cdlemk12u  40911  cdlemk7u-2N  40927  cdlemk11u-2N  40928  cdlemk12u-2N  40929  cdlemk20-2N  40931  cdlemk22  40932  cdlemk22-3  40940  cdlemk33N  40948  cdlemk53b  40995  cdlemk53  40996  cdlemk55a  40998  cdlemkyyN  41001  cdlemk43N  41002