Theorem imim12i 53

Description: Inference joining two implications. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 29-Oct-2011.)

Hypotheses

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

Assertion

Ref	Expression
imim12i	|- ( ( ps -> ch ) -> ( ph -> th ) )

Proof of Theorem imim12i

Step	Hyp	Ref	Expression
1		imim12i.1	. 2 |- ( ph -> ps )
2		imim12i.2	. . 3 |- ( ch -> th )
3	2	imim2i 12	. 2 |- ( ( ps -> ch ) -> ( ps -> th ) )
4	1, 3	syl5 28	1 |- ( ( ps -> ch ) -> ( ph -> th ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7

This theorem is referenced by:  imim1i  54  hbim  1437  19.38  1566  cbvexdh  1801  exmoeudc  1963  bj-bdfindis  10072