Theorem wl-ax2 33264

Description: ax-2 7 proved from Lukasiewicz's axioms. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-ax2	|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )

Proof of Theorem wl-ax2

Step	Hyp	Ref	Expression
1		wl-pm2.21 33259	. . 3 |- ( -. ph -> ( ph -> ch ) )
2	1	wl-a1d 33263	. 2 |- ( -. ph -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
3		wl-imim2 33262	. 2 |- ( ( ps -> ch ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
4	2, 3	wl-ja 33261	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )

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-pm2.04  33267