Metamath Proof Explorer


Theorem bi23impib

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

Ref Expression
Hypothesis bi23impib.1
|- ( ph -> ( ( ps /\ ch ) <-> th ) )
Assertion bi23impib
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi23impib.1
 |-  ( ph -> ( ( ps /\ ch ) <-> th ) )
2 1 biimpd
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )
3 2 3impib
 |-  ( ( ph /\ ps /\ ch ) -> th )