Theorem syl6rbb

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

	Ref	Expression
Hypotheses	syl6rbb.1	|- ( ph -> ( ps <-> ch ) )
	syl6rbb.2	|- ( ch <-> th )
Assertion	syl6rbb	|- ( ph -> ( th <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		syl6rbb.1	|- ( ph -> ( ps <-> ch ) )
2		syl6rbb.2	|- ( ch <-> th )
3	1 2	syl6bb	|- ( ph -> ( ps <-> th ) )
4	3	bicomd	|- ( ph -> ( th <-> ps ) )