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 1136	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1088

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 398  df-3an 1090

This theorem is referenced by:  ivthALT  35220  dalemclpjs  38505  dath2  38608  cdlema1N  38662  cdlemk7u  39741  cdlemk11u  39742  cdlemk12u  39743  cdlemk22  39764  cdlemk23-3  39773  cdlemk24-3  39774  cdlemk33N  39780  cdlemk11ta  39800  cdlemk11tc  39816  cdlemk54  39829