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	$$⊢\left(\left(\phi ,\psi \right)\to \chi \right)$$
Assertion	int2	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		int2.1	$$⊢\left(\left(\phi ,\psi \right)\to \chi \right)$$
2	1	dfvd2ani	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
3	2	ex	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3	dfvd1ir	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)$$