Theorem simp112 1085

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

Assertion

Ref	Expression
simp112	⊢ ((((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) ∧ η ∧ ζ) → ψ)

Proof of Theorem simp112

Step	Hyp	Ref	Expression
1		simp12 986	. 2 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) → ψ)
2	1	3ad2ant1 976	1 ⊢ ((((φ ∧ ψ ∧ χ) ∧ θ ∧ τ) ∧ η ∧ ζ) → ψ)

Syntax hints:   → wi 4   ∧ 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)