Metamath Proof Explorer


Theorem bitr2di

Description: A syllogism inference from two biconditionals. (Contributed by NM, 5-Aug-1993)

Ref Expression
Hypotheses bitr2di.1
|- ( ph -> ( ps <-> ch ) )
bitr2di.2
|- ( ch <-> th )
Assertion bitr2di
|- ( ph -> ( th <-> ps ) )

Proof

Step Hyp Ref Expression
1 bitr2di.1
 |-  ( ph -> ( ps <-> ch ) )
2 bitr2di.2
 |-  ( ch <-> th )
3 1 2 bitrdi
 |-  ( ph -> ( ps <-> th ) )
4 3 bicomd
 |-  ( ph -> ( th <-> ps ) )