Theorem simp-6r 747

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-6r	⊢ (((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) → ψ)

Proof of Theorem simp-6r

Step	Hyp	Ref	Expression
1		simp-5r 745	. 2 ⊢ ((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) → ψ)
2	1	adantr 451	1 ⊢ (((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) → ψ)

Syntax hints:   → wi 4   ∧ wa 358

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

This theorem is referenced by:  simp-7r  749