Theorem dfvd2ir

Description: Right-to-left inference form of dfvd2 . (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfvd2ir.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	dfvd2ir	$$⊢\left(\phi ,\psi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dfvd2ir.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		dfvd2	$$⊢\left(\phi ,\psi \to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$
3	1 2	mpbir	$$⊢\left(\phi ,\psi \to \chi \right)$$