Theorem syl5imp 38718

Description: Closed form of syl5 34. Derived automatically from syl5impVD 39099. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
syl5imp	|- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) )

Proof of Theorem syl5imp

Step	Hyp	Ref	Expression
1		pm2.04 90	. . 3 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )
2	1	imim2d 57	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ps ) -> ( th -> ( ph -> ch ) ) ) )
3	2	com34 91	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) )

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)