Theorem imim12i

Description: Inference joining two implications. Inference associated with imim12 . Its associated inference is 3syl . (Contributed by NM, 12-Mar-1993) (Proof shortened by Mel L. O'Cat, 29-Oct-2011)

	Ref	Expression
Hypotheses	imim12i.1	|- ( ph -> ps )
	imim12i.2	|- ( ch -> th )
Assertion	imim12i	|- ( ( ps -> ch ) -> ( ph -> th ) )

Proof

Step	Hyp	Ref	Expression
1		imim12i.1	|- ( ph -> ps )
2		imim12i.2	|- ( ch -> th )
3	2	imim2i	|- ( ( ps -> ch ) -> ( ps -> th ) )
4	1 3	syl5	|- ( ( ps -> ch ) -> ( ph -> th ) )