Theorem syl7bi

Description: A mixed syllogism inference from a doubly nested implication and a biconditional. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypotheses	syl7bi.1	|- ( ph <-> ps )
	syl7bi.2	|- ( ch -> ( th -> ( ps -> ta ) ) )
Assertion	syl7bi	|- ( ch -> ( th -> ( ph -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		syl7bi.1	|- ( ph <-> ps )
2		syl7bi.2	|- ( ch -> ( th -> ( ps -> ta ) ) )
3	1	biimpi	|- ( ph -> ps )
4	3 2	syl7	|- ( ch -> ( th -> ( ph -> ta ) ) )