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Metamath Proof Explorer

Theorem 3expia

Description: Exportation from triple conjunction. (Contributed by NM, 19-May-2007) (Proof shortened by Wolf Lammen, 22-Jun-2022)

		Ref	Expression
	Hypothesis	3exp.1	$⊢ (φ \land ψ \land χ) \to θ$
	Assertion	3expia	$⊢ (φ \land ψ) \to (χ \to θ)$

Step	Hyp	Ref	Expression
1		3exp.1	$⊢ (φ \land ψ \land χ) \to θ$
2	1	3expb	$⊢ (φ \land (ψ \land χ)) \to θ$
3	2	expr	$⊢ (φ \land ψ) \to (χ \to θ)$