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Metamath Proof Explorer

Theorem impancom

Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013)

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

Step	Hyp	Ref	Expression
1		impancom.1	$⊢ (φ \land ψ) \to (χ \to θ)$
2	1	ex	$⊢ φ \to (ψ \to (χ \to θ))$
3	2	com23	$⊢ φ \to (χ \to (ψ \to θ))$
4	3	imp	$⊢ (φ \land χ) \to (ψ \to θ)$