Theorem bitr3id

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

	Ref	Expression
Hypotheses	bitr3id.1	|- ( ps <-> ph )
	bitr3id.2	|- ( ch -> ( ps <-> th ) )
Assertion	bitr3id	|- ( ch -> ( ph <-> th ) )

Proof

Step	Hyp	Ref	Expression
1		bitr3id.1	|- ( ps <-> ph )
2		bitr3id.2	|- ( ch -> ( ps <-> th ) )
3	1	bicomi	|- ( ph <-> ps )
4	3 2	syl5bb	|- ( ch -> ( ph <-> th ) )