Theorem wl-syl 33246

Description: An inference version of the transitive laws for implication luk-1 1580. Copy of syl 17 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
wl-syl.1	|- ( ph -> ps )
wl-syl.2	|- ( ps -> ch )

Assertion

Ref	Expression
wl-syl	|- ( ph -> ch )

Proof of Theorem wl-syl

Step	Hyp	Ref	Expression
1		wl-syl.2	. 2 |- ( ps -> ch )
2		wl-syl.1	. . 3 |- ( ph -> ps )
3	2	wl-imim1i 33245	. 2 |- ( ( ps -> ch ) -> ( ph -> ch ) )
4	1, 3	ax-mp 5	1 |- ( ph -> ch )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241

This theorem is referenced by:  wl-syl5  33247  wl-pm2.18d  33248  wl-syl6  33254  wl-ax1  33256  wl-pm2.27  33257  wl-a1d  33263  wl-id  33265