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Metamath Proof Explorer

Theorem simpl31

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

		Ref	Expression
	Assertion	simpl31	$⊢ ((θ \land τ \land (φ \land ψ \land χ)) \land η) \to φ$

Step	Hyp	Ref	Expression
1		simpl1	$⊢ ((φ \land ψ \land χ) \land η) \to φ$
2	1	3ad2antl3	$⊢ ((θ \land τ \land (φ \land ψ \land χ)) \land η) \to φ$