Theorem simp331 1323

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 1206	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1132	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1084

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 206  df-an 395  df-3an 1086

This theorem is referenced by:  ivthALT  35852  dalemclpjs  39139  dath2  39242  cdlema1N  39296  cdlemk7u  40375  cdlemk11u  40376  cdlemk12u  40377  cdlemk22  40398  cdlemk23-3  40407  cdlemk24-3  40408  cdlemk33N  40414  cdlemk11ta  40434  cdlemk11tc  40450  cdlemk54  40463