Theorem simp211 1313

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 1205	. 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 1087

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 1089

This theorem is referenced by:  cdleme27a  40740  cdlemk5u  41234  cdlemk6u  41235  cdlemk7u  41243  cdlemk11u  41244  cdlemk12u  41245  cdlemk7u-2N  41261  cdlemk11u-2N  41262  cdlemk12u-2N  41263  cdlemk20-2N  41265  cdlemk22  41266  cdlemk33N  41282  cdlemk53b  41329  cdlemk53  41330  cdlemk55a  41332  cdlemkyyN  41335  cdlemk43N  41336