Theorem simp12r 1069

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

Assertion

Ref	Expression
simp12r	⊢ (((χ ∧ (φ ∧ ψ) ∧ θ) ∧ τ ∧ η) → ψ)

Proof of Theorem simp12r

Step	Hyp	Ref	Expression
1		simp2r 982	. 2 ⊢ ((χ ∧ (φ ∧ ψ) ∧ θ) → ψ)
2	1	3ad2ant1 976	1 ⊢ (((χ ∧ (φ ∧ ψ) ∧ θ) ∧ τ ∧ 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:  sfinltfin  4535