Theorem simp-7r 749

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

Assertion

Ref	Expression
simp-7r	⊢ ((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) → ψ)

Proof of Theorem simp-7r

Step	Hyp	Ref	Expression
1		simp-6r 747	. 2 ⊢ (((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) → ψ)
2	1	adantr 451	1 ⊢ ((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) → 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-8r  751