Metamath Proof Explorer


Theorem bitrdi

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

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

Proof

Step Hyp Ref Expression
1 bitrdi.1
 |-  ( ph -> ( ps <-> ch ) )
2 bitrdi.2
 |-  ( ch <-> th )
3 2 a1i
 |-  ( ph -> ( ch <-> th ) )
4 1 3 bitrd
 |-  ( ph -> ( ps <-> th ) )