Theorem simp331 1327

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 1210	. 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 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:  ivthALT  36330  dalemclpjs  39635  dath2  39738  cdlema1N  39792  cdlemk7u  40871  cdlemk11u  40872  cdlemk12u  40873  cdlemk22  40894  cdlemk23-3  40903  cdlemk24-3  40904  cdlemk33N  40910  cdlemk11ta  40930  cdlemk11tc  40946  cdlemk54  40959