Theorem wl-pm2.18d 33248

Description: Deduction based on reductio ad absurdum. Copy of pm2.18d 124 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-pm2.18d.1	|- ( ph -> ( -. ps -> ps ) )

Assertion

Ref	Expression
wl-pm2.18d	|- ( ph -> ps )

Proof of Theorem wl-pm2.18d

Step	Hyp	Ref	Expression
1		wl-pm2.18d.1	. 2 |- ( ph -> ( -. ps -> ps ) )
2		ax-luk2 33242	. 2 |- ( ( -. ps -> ps ) -> ps )
3	1, 2	wl-syl 33246	1 |- ( ph -> ps )

Syntax hints:   -. wn 3   -> wi 4

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

This theorem is referenced by:  wl-con4i  33249  wl-mpi  33252  wl-con1i  33260  wl-ja  33261