Theorem simp-8r 751

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

Assertion

Ref	Expression
simp-8r	⊢ (((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) → ψ)

Proof of Theorem simp-8r

Step	Hyp	Ref	Expression
1		simp-7r 749	. 2 ⊢ ((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) → ψ)
2	1	adantr 451	1 ⊢ (((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) → ψ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  simp-9r  753