This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm5.32ri

Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 12-Mar-1995)

Ref Expression
Hypothesis pm5.32i.1 
|- ( ph -> ( ps <-> ch ) )
Assertion pm5.32ri 
|- ( ( ps /\ ph ) <-> ( ch /\ ph ) )

Proof

Step Hyp Ref Expression
1 pm5.32i.1 
 |-  ( ph -> ( ps <-> ch ) )
2 1 pm5.32i 
 |-  ( ( ph /\ ps ) <-> ( ph /\ ch ) )
3 ancom 
 |-  ( ( ps /\ ph ) <-> ( ph /\ ps ) )
4 ancom 
 |-  ( ( ch /\ ph ) <-> ( ph /\ ch ) )
5 2 3 4 3bitr4i 
 |-  ( ( ps /\ ph ) <-> ( ch /\ ph ) )