Theorem simp331 1333

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 1216	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑)
2	1	3ad2ant3 1141	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1092

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 208  df-an 397  df-3an 1094

This theorem is referenced by:  ivthALT  36563  dalemclpjs  40126  dath2  40229  cdlema1N  40283  cdlemk7u  41362  cdlemk11u  41363  cdlemk12u  41364  cdlemk22  41385  cdlemk23-3  41394  cdlemk24-3  41395  cdlemk33N  41401  cdlemk11ta  41421  cdlemk11tc  41437  cdlemk54  41450