Theorem wl-syl6 33254

Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. Copy of syl6 35 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
wl-syl6.1	|- ( ph -> ( ps -> ch ) )
wl-syl6.2	|- ( ch -> th )

Assertion

Ref	Expression
wl-syl6	|- ( ph -> ( ps -> th ) )

Proof of Theorem wl-syl6

Step	Hyp	Ref	Expression
1		wl-syl6.1	. 2 |- ( ph -> ( ps -> ch ) )
2		wl-syl6.2	. . 3 |- ( ch -> th )
3	2	wl-imim2i 33253	. 2 |- ( ( ps -> ch ) -> ( ps -> th ) )
4	1, 3	wl-syl 33246	1 |- ( ph -> ( ps -> th ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243

This theorem is referenced by:  wl-ax3  33255  wl-pm2.27  33257