Metamath Proof Explorer

Theorem simp-11l

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

		Ref	Expression
	Assertion	simp-11l	$⊢ (((((((((((φ \land ψ) \land χ) \land θ) \land τ) \land η) \land ζ) \land σ) \land ρ) \land μ) \land λ) \land κ) \to φ$

Step	Hyp	Ref	Expression
1		simpl	$⊢ (φ \land ψ) \to φ$
2	1	ad10antr	$⊢ (((((((((((φ \land ψ) \land χ) \land θ) \land τ) \land η) \land ζ) \land σ) \land ρ) \land μ) \land λ) \land κ) \to φ$