Metamath Proof Explorer

Theorem simpl12

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 24-Jun-2022)

		Ref	Expression
	Assertion	simpl12	$⊢ (((φ \land ψ \land χ) \land θ \land τ) \land η) \to ψ$

Step	Hyp	Ref	Expression
1		simpl2	$⊢ ((φ \land ψ \land χ) \land η) \to ψ$
2	1	3ad2antl1	$⊢ (((φ \land ψ \land χ) \land θ \land τ) \land η) \to ψ$