Metamath Proof Explorer

Theorem biimparc

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

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

Proof

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