Theorem sylbi

Description: A mixed syllogism inference from a biconditional and an implication. Useful for substituting an antecedent with a definition. (Contributed by NM, 3-Jan-1993)

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

Proof

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