Metamath Proof Explorer

Theorem simp-8r

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 24-May-2022)

		Ref	Expression
	Assertion	simp-8r	$⊢ ((((((((φ \land ψ) \land χ) \land θ) \land τ) \land η) \land ζ) \land σ) \land ρ) \to ψ$

Step	Hyp	Ref	Expression
1		id	$⊢ ψ \to ψ$
2	1	ad8antlr	$⊢ ((((((((φ \land ψ) \land χ) \land θ) \land τ) \land η) \land ζ) \land σ) \land ρ) \to ψ$