Theorem syl5rbb

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

	Ref	Expression
Hypotheses	syl5rbb.1	|- ( ph <-> ps )
	syl5rbb.2	|- ( ch -> ( ps <-> th ) )
Assertion	syl5rbb	|- ( ch -> ( th <-> ph ) )

Proof

Step	Hyp	Ref	Expression
1		syl5rbb.1	|- ( ph <-> ps )
2		syl5rbb.2	|- ( ch -> ( ps <-> th ) )
3	1 2	syl5bb	|- ( ch -> ( ph <-> th ) )
4	3	bicomd	|- ( ch -> ( th <-> ph ) )