Theorem simp211 1328

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 1220	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)
2	1	3ad2ant2 1150	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1101

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 401  df-3an 1103

This theorem is referenced by:  cdleme27a  41026  cdlemk5u  41520  cdlemk6u  41521  cdlemk7u  41529  cdlemk11u  41530  cdlemk12u  41531  cdlemk7u-2N  41547  cdlemk11u-2N  41548  cdlemk12u-2N  41549  cdlemk20-2N  41551  cdlemk22  41552  cdlemk33N  41568  cdlemk53b  41615  cdlemk53  41616  cdlemk55a  41618  cdlemkyyN  41621  cdlemk43N  41622