Theorem syl6rbbr

Description: A syllogism inference from two biconditionals. (Contributed by NM, 25-Nov-1994)

	Ref	Expression
Hypotheses	syl6rbbr.1	|- ( ph -> ( ps <-> ch ) )
	syl6rbbr.2	|- ( th <-> ch )
Assertion	syl6rbbr	|- ( ph -> ( th <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		syl6rbbr.1	|- ( ph -> ( ps <-> ch ) )
2		syl6rbbr.2	|- ( th <-> ch )
3	2	bicomi	|- ( ch <-> th )
4	1 3	syl6rbb	|- ( ph -> ( th <-> ps ) )