Theorem simp331 1326

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

Assertion

Ref	Expression
simp331	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Proof of Theorem simp331

Step	Hyp	Ref	Expression
1		simp31 1209	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 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:  ivthALT  36301  dalemclpjs  39591  dath2  39694  cdlema1N  39748  cdlemk7u  40827  cdlemk11u  40828  cdlemk12u  40829  cdlemk22  40850  cdlemk23-3  40859  cdlemk24-3  40860  cdlemk33N  40866  cdlemk11ta  40886  cdlemk11tc  40902  cdlemk54  40915