Theorem syl6ib

Description: A mixed syllogism inference from a nested implication and a biconditional. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	syl6ib.1	|- ( ph -> ( ps -> ch ) )
	syl6ib.2	|- ( ch <-> th )
Assertion	syl6ib	|- ( ph -> ( ps -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl6ib.1	|- ( ph -> ( ps -> ch ) )
2		syl6ib.2	|- ( ch <-> th )
3	2	biimpi	|- ( ch -> th )
4	1 3	syl6	|- ( ph -> ( ps -> th ) )