Metamath Proof Explorer


Theorem dfvd1impr

Description: Right-to-left part of definition of virtual deduction. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion dfvd1impr
|- ( ( ph -> ps ) -> (. ph ->. ps ). )

Proof

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