Theorem simp332 1344

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

Assertion

Ref	Expression
simp332	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simp332

Step	Hyp	Ref	Expression
1		simp32 1227	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1151	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  ivthALT  36731  dalemclqjt  40294  dath2  40396  cdlema1N  40450  cdleme26eALTN  41020  cdlemk7u  41529  cdlemk11u  41530  cdlemk12u  41531  cdlemk23-3  41561  cdlemk33N  41568  cdlemk11ta  41588  cdlemk11tc  41604  cdlemk54  41617