Theorem wl-pm2.27 33257

Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens ax-mp 5. Theorem *2.27 of [WhiteheadRussell] p. 104. Copy of pm2.27 42 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-pm2.27	|- ( ph -> ( ( ph -> ps ) -> ps ) )

Proof of Theorem wl-pm2.27

Step	Hyp	Ref	Expression
1		wl-ax1 33256	. . 3 |- ( ph -> ( -. ps -> ph ) )
2		ax-luk1 33241	. . 3 |- ( ( -. ps -> ph ) -> ( ( ph -> ps ) -> ( -. ps -> ps ) ) )
3	1, 2	wl-syl 33246	. 2 |- ( ph -> ( ( ph -> ps ) -> ( -. ps -> ps ) ) )
4		ax-luk2 33242	. 2 |- ( ( -. ps -> ps ) -> ps )
5	3, 4	wl-syl6 33254	1 |- ( ph -> ( ( ph -> ps ) -> ps ) )

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-com12  33258