Metamath Proof Explorer


Theorem dfvd2impr

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

Ref Expression
Assertion dfvd2impr
|- ( ( ph -> ( ps -> ch ) ) -> (. ph ,. ps ->. ch ). )

Proof

Step Hyp Ref Expression
1 dfvd2
 |-  ( (. ph ,. ps ->. ch ). <-> ( ph -> ( ps -> ch ) ) )
2 1 biimpri
 |-  ( ( ph -> ( ps -> ch ) ) -> (. ph ,. ps ->. ch ). )