Metamath Proof Explorer


Theorem biimpa

Description: Importation inference from a logical equivalence. (Contributed by NM, 3-May-1994)

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

Proof

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