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Metamath Proof Explorer

Theorem int2

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 is ex . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	int2.1	$⊢ ((φ, ψ) \to χ)$
	Assertion	int2	$⊢ (φ \to (ψ \to χ))$

Proof

Step	Hyp	Ref	Expression
1		int2.1	$⊢ ((φ, ψ) \to χ)$
2	1	dfvd2ani	$⊢ (φ \land ψ) \to χ$
3	2	ex	$⊢ φ \to (ψ \to χ)$
4	3	dfvd1ir	$⊢ (φ \to (ψ \to χ))$