Metamath Proof Explorer

Theorem bi23imp13

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

Ref Expression
Hypothesis bi23imp13.1 
|- ( ph -> ( ps <-> ( ch -> th ) ) )
Assertion bi23imp13 
|- ( ( ph /\ ps /\ ch ) -> th )

Proof

Step Hyp Ref Expression
1 bi23imp13.1 
 |-  ( ph -> ( ps <-> ( ch -> th ) ) )
2 1 biimpd 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
3 2 3imp 
 |-  ( ( ph /\ ps /\ ch ) -> th )