Metamath Proof Explorer


Theorem biimpac

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

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

Proof

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