Theorem syl5ibcom

Description: A mixed syllogism inference. (Contributed by NM, 19-Jun-2007)

	Ref	Expression
Hypotheses	syl5ib.1	|- ( ph -> ps )
	syl5ib.2	|- ( ch -> ( ps <-> th ) )
Assertion	syl5ibcom	|- ( ph -> ( ch -> th ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ib.1	|- ( ph -> ps )
2		syl5ib.2	|- ( ch -> ( ps <-> th ) )
3	1 2	syl5ib	|- ( ch -> ( ph -> th ) )
4	3	com12	|- ( ph -> ( ch -> th ) )