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Metamath Proof Explorer

Theorem dfvd2imp

Description: The virtual deduction form of a 2-antecedent nested implication implies the 2-antecedent nested implication. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	dfvd2imp	$⊢ (φ, ψ \to χ) \to (φ \to (ψ \to χ))$

Proof

Step	Hyp	Ref	Expression
1		dfvd2	$⊢ (φ, ψ \to χ) \leftrightarrow (φ \to (ψ \to χ))$
2	1	biimpi	$⊢ (φ, ψ \to χ) \to (φ \to (ψ \to χ))$