Metamath Proof Explorer


Theorem bi13impia

Description: 3impia with the outer implication of the hypothesis a biconditional. (Contributed by Alan Sare, 6-Nov-2017)

Ref Expression
Hypothesis bi13impia.1
|- ( ( ph /\ ps ) <-> ( ch -> th ) )
Assertion bi13impia
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi13impia.1
 |-  ( ( ph /\ ps ) <-> ( ch -> th ) )
2 1 biimpi
 |-  ( ( ph /\ ps ) -> ( ch -> th ) )
3 2 3impia
 |-  ( ( ph /\ ps /\ ch ) -> th )