Theorem simpl31 1036

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

Assertion

Ref	Expression
simpl31	⊢ (((θ ∧ τ ∧ (φ ∧ ψ ∧ χ)) ∧ η) → φ)

Proof of Theorem simpl31

Step	Hyp	Ref	Expression
1		simp31 991	. 2 ⊢ ((θ ∧ τ ∧ (φ ∧ ψ ∧ χ)) → φ)
2	1	adantr 451	1 ⊢ (((θ ∧ τ ∧ (φ ∧ ψ ∧ χ)) ∧ η) → 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:  tfin11  4493