Theorem simpl32 1037

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

Assertion

Ref	Expression
simpl32	⊢ (((θ ∧ τ ∧ (φ ∧ ψ ∧ χ)) ∧ η) → ψ)

Proof of Theorem simpl32

Step	Hyp	Ref	Expression
1		simp32 992	. 2 ⊢ ((θ ∧ τ ∧ (φ ∧ ψ ∧ χ)) → ψ)
2	1	adantr 451	1 ⊢ (((θ ∧ τ ∧ (φ ∧ ψ ∧ χ)) ∧ η) → ψ)

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:  tfin11  4494