Metamath Proof Explorer


Theorem bitr4di

Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)

Ref Expression
Hypotheses bitr4di.1
|- ( ph -> ( ps <-> ch ) )
bitr4di.2
|- ( th <-> ch )
Assertion bitr4di
|- ( ph -> ( ps <-> th ) )

Proof

Step Hyp Ref Expression
1 bitr4di.1
 |-  ( ph -> ( ps <-> ch ) )
2 bitr4di.2
 |-  ( th <-> ch )
3 2 bicomi
 |-  ( ch <-> th )
4 1 3 bitrdi
 |-  ( ph -> ( ps <-> th ) )