Theorem sylibr

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

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

Proof

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