Theorem wl-notnotr 33266

Description: Converse of double negation. Theorem *2.14 of [WhiteheadRussell] p. 102. In classical logic (our logic) this is always true. In intuitionistic logic this is not always true; in intuitionistic logic, when this is true for some ph, then ph is stable. Copy of notnotr 125 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-notnotr	|- ( -. -. ph -> ph )

Proof of Theorem wl-notnotr

Step	Hyp	Ref	Expression
1		wl-id 33265	. 2 |- ( -. ph -> -. ph )
2	1	wl-con1i 33260	1 |- ( -. -. ph -> 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: (None)