Metamath Proof Explorer


Theorem ibdr

Description: Reverse of ibd . (Contributed by Rodolfo Medina, 30-Sep-2010)

Ref Expression
Hypothesis ibdr.1
|- ( ph -> ( ch -> ( ps <-> ch ) ) )
Assertion ibdr
|- ( ph -> ( ch -> ps ) )

Proof

Step Hyp Ref Expression
1 ibdr.1
 |-  ( ph -> ( ch -> ( ps <-> ch ) ) )
2 1 bicomdd
 |-  ( ph -> ( ch -> ( ch <-> ps ) ) )
3 2 ibd
 |-  ( ph -> ( ch -> ps ) )