Theorem syl6ibr

Description: A mixed syllogism inference from a nested implication and a biconditional. Useful for substituting an embedded consequent with a definition. (Contributed by NM, 10-Jan-1993)

	Ref	Expression
Hypotheses	syl6ibr.1	|- ( ph -> ( ps -> ch ) )
	syl6ibr.2	|- ( th <-> ch )
Assertion	syl6ibr	|- ( ph -> ( ps -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl6ibr.1	|- ( ph -> ( ps -> ch ) )
2		syl6ibr.2	|- ( th <-> ch )
3	2	biimpri	|- ( ch -> th )
4	1 3	syl6	|- ( ph -> ( ps -> th ) )