Theorem dfvd2imp

Description: The virtual deduction form of a 2-antecedent nested implication implies the 2-antecedent nested implication. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd2imp	$$⊢\left(\phi ,\psi \to \chi \right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$

Proof

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