Theorem dfvd2

Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd2	$$⊢\left(\phi ,\psi \to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-vd2	$$⊢\left(\phi ,\psi \to \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\to \chi \right)$$
2		impexp	$$⊢\left(\left(\phi \wedge \psi \right)\to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$
3	1 2	bitri	$$⊢\left(\phi ,\psi \to \chi \right)\leftrightarrow \left(\phi \to \left(\psi \to \chi \right)\right)$$