Metamath Proof Explorer


Theorem dfvd2ir

Description: Right-to-left inference form of dfvd2 . (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis dfvd2ir.1
|- ( ph -> ( ps -> ch ) )
Assertion dfvd2ir
|- (. ph ,. ps ->. ch ).

Proof

Step Hyp Ref Expression
1 dfvd2ir.1
 |-  ( ph -> ( ps -> ch ) )
2 dfvd2
 |-  ( (. ph ,. ps ->. ch ). <-> ( ph -> ( ps -> ch ) ) )
3 1 2 mpbir
 |-  (. ph ,. ps ->. ch ).