Theorem int3

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 is 3expia . (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	int3.1	$$⊢\left(\left(\phi ,\psi ,\chi \right)\to \theta \right)$$
Assertion	int3	$$⊢\left(\left(\phi ,\psi \right)\to \left(\chi \to \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		int3.1	$$⊢\left(\left(\phi ,\psi ,\chi \right)\to \theta \right)$$
2	1	dfvd3ani	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
3	2	3expia	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
4	3	dfvd2anir	$$⊢\left(\left(\phi ,\psi \right)\to \left(\chi \to \theta \right)\right)$$