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 1134	1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑)

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  40361  cdlemk5u  40855  cdlemk6u  40856  cdlemk7u  40864  cdlemk11u  40865  cdlemk12u  40866  cdlemk7u-2N  40882  cdlemk11u-2N  40883  cdlemk12u-2N  40884  cdlemk20-2N  40886  cdlemk22  40887  cdlemk33N  40903  cdlemk53b  40950  cdlemk53  40951  cdlemk55a  40953  cdlemkyyN  40956  cdlemk43N  40957