Theorem bitr2id

Description: A syllogism inference from two biconditionals. (Contributed by NM, 1-Aug-1993)

	Ref	Expression
Hypotheses	bitr2id.1	|- ( ph <-> ps )
	bitr2id.2	|- ( ch -> ( ps <-> th ) )
Assertion	bitr2id	|- ( ch -> ( th <-> ph ) )

Proof

Step	Hyp	Ref	Expression
1		bitr2id.1	|- ( ph <-> ps )
2		bitr2id.2	|- ( ch -> ( ps <-> th ) )
3	1 2	syl5bb	|- ( ch -> ( ph <-> th ) )
4	3	bicomd	|- ( ch -> ( th <-> ph ) )