Theorem simp3l2 1382

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

Assertion

Ref	Expression
simp3l2	⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Proof of Theorem simp3l2

Step	Hyp	Ref	Expression
1		simpl2 1248	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)
2	1	3ad2ant3 1169	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 386   ∧ w3a 1111

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 199  df-an 387  df-3an 1113

This theorem is referenced by:  cvmlift2lem10  31829  cdleme36m  36529  cdlemk5u  36929  cdlemk6u  36930  cdlemk21N  36941  cdlemk20  36942  cdlemk27-3  36975  cdlemk28-3  36976