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	|- ( ph -> ps )
Assertion	dfvd1ir	|- (. ph ->. ps ).

Proof

Step	Hyp	Ref	Expression
1		dfvd1ir.1	|- ( ph -> ps )
2		df-vd1	|- ( (. ph ->. ps ). <-> ( ph -> ps ) )
3	1 2	mpbir	|- (. ph ->. ps ).