Theorem imim12 100

Description: Closed form of imim12i 59 and of 3syl 18. (Contributed by BJ, 16-Jul-2019.)

Assertion

Ref	Expression
imim12	|- ( ( ph -> ps ) -> ( ( ch -> th ) -> ( ( ps -> ch ) -> ( ph -> th ) ) ) )

Proof of Theorem imim12

Step	Hyp	Ref	Expression
1		imim2 55	. . . 4 |- ( ( ch -> th ) -> ( ( ps -> ch ) -> ( ps -> th ) ) )
2	1	com13 83	. . 3 |- ( ps -> ( ( ps -> ch ) -> ( ( ch -> th ) -> th ) ) )
3	2	imim2i 16	. 2 |- ( ( ph -> ps ) -> ( ph -> ( ( ps -> ch ) -> ( ( ch -> th ) -> th ) ) ) )
4	3	com24 90	1 |- ( ( ph -> ps ) -> ( ( ch -> th ) -> ( ( ps -> ch ) -> ( ph -> th ) ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by: (None)