Theorem sylib

Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by NM, 3-Jan-1993)

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

Proof

Step	Hyp	Ref	Expression
1		sylib.1	|- ( ph -> ps )
2		sylib.2	|- ( ps <-> ch )
3	2	biimpi	|- ( ps -> ch )
4	1 3	syl	|- ( ph -> ch )