Metamath Proof Explorer

Theorem biimpar

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

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

Proof

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