Metamath Proof Explorer


Theorem bi13impib

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

Ref Expression
Hypothesis bi13impib.1
|- ( ph <-> ( ( ps /\ ch ) -> th ) )
Assertion bi13impib
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi13impib.1
 |-  ( ph <-> ( ( ps /\ ch ) -> th ) )
2 1 biimpi
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )
3 2 3impib
 |-  ( ( ph /\ ps /\ ch ) -> th )