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 ) )