Theorem simp-11l 756

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

Assertion

Ref	Expression
simp-11l	⊢ ((((((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) ∧ μ) ∧ λ) ∧ κ) → φ)

Proof of Theorem simp-11l

Step	Hyp	Ref	Expression
1		simp-10l 754	. 2 ⊢ (((((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) ∧ μ) ∧ λ) → φ)
2	1	adantr 451	1 ⊢ ((((((((((((φ ∧ ψ) ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) ∧ μ) ∧ λ) ∧ κ) → φ)

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: (None)