Metamath Proof Explorer


Theorem 3impexpbicomi

Description: Inference associated with 3impexpbicom . Derived automatically from 3impexpbicomiVD . (Contributed by Alan Sare, 31-Dec-2011)

Ref Expression
Hypothesis 3impexpbicomi.1
|- ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )
Assertion 3impexpbicomi
|- ( ph -> ( ps -> ( ch -> ( ta <-> th ) ) ) )

Proof

Step Hyp Ref Expression
1 3impexpbicomi.1
 |-  ( ( ph /\ ps /\ ch ) -> ( th <-> ta ) )
2 1 bicomd
 |-  ( ( ph /\ ps /\ ch ) -> ( ta <-> th ) )
3 2 3exp
 |-  ( ph -> ( ps -> ( ch -> ( ta <-> th ) ) ) )