Theorem dfvd1ir

Description: Inference form of df-vd1 with the virtual deduction as the assertion. (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfvd1ir.1	$$⊢\phi \to \psi$$
Assertion	dfvd1ir	$$⊢\left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dfvd1ir.1	$$⊢\phi \to \psi$$
2		df-vd1	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\phi \to \psi \right)$$
3	1 2	mpbir	$$⊢\left(\phi \to \psi \right)$$