Theorem simp211 1312

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp211	⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp211

Step	Hyp	Ref	Expression
1		simp11 1204	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1135	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1088

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 210  df-an 400  df-3an 1090

This theorem is referenced by:  cdleme27a  38001  cdlemk5u  38495  cdlemk6u  38496  cdlemk7u  38504  cdlemk11u  38505  cdlemk12u  38506  cdlemk7u-2N  38522  cdlemk11u-2N  38523  cdlemk12u-2N  38524  cdlemk20-2N  38526  cdlemk22  38527  cdlemk33N  38543  cdlemk53b  38590  cdlemk53  38591  cdlemk55a  38593  cdlemkyyN  38596  cdlemk43N  38597