Theorem simp31l 1078

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

Assertion

Ref	Expression
simp31l	⊢ ((τ ∧ η ∧ ((φ ∧ ψ) ∧ χ ∧ θ)) → φ)

Proof of Theorem simp31l

Step	Hyp	Ref	Expression
1		simp1l 979	. 2 ⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → φ)
2	1	3ad2ant3 978	1 ⊢ ((τ ∧ η ∧ ((φ ∧ ψ) ∧ χ ∧ θ)) → φ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by: (None)