Theorem wl-con4i 33249

Description: Inference rule. Copy of con4i 113 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-con4i.1	|- ( -. ph -> -. ps )

Assertion

Ref	Expression
wl-con4i	|- ( ps -> ph )

Proof of Theorem wl-con4i

Step	Hyp	Ref	Expression
1		wl-con4i.1	. . 3 |- ( -. ph -> -. ps )
2		ax-luk3 33243	. . 3 |- ( ps -> ( -. ps -> ph ) )
3	1, 2	wl-syl5 33247	. 2 |- ( ps -> ( -. ph -> ph ) )
4	3	wl-pm2.18d 33248	1 |- ( ps -> ph )

Syntax hints:   -. wn 3   -> 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-a1i  33251