Theorem syl5ibr

Description: A mixed syllogism inference. (Contributed by NM, 3-Apr-1994)

	Ref	Expression
Hypotheses	syl5ibr.1	|- ( ph -> th )
	syl5ibr.2	|- ( ch -> ( ps <-> th ) )
Assertion	syl5ibr	|- ( ch -> ( ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ibr.1	|- ( ph -> th )
2		syl5ibr.2	|- ( ch -> ( ps <-> th ) )
3	2	bicomd	|- ( ch -> ( th <-> ps ) )
4	1 3	syl5ib	|- ( ch -> ( ph -> ps ) )