Theorem wl-luk-ax2

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

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

Proof

Step	Hyp	Ref	Expression
1		wl-luk-pm2.21	|- ( -. ph -> ( ph -> ch ) )
2	1	wl-luk-a1d	|- ( -. ph -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
3		wl-luk-imim2	|- ( ( ps -> ch ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
4	2 3	wl-luk-ja	|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )