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Theorem wl-notnotr 32442
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 𝜑, then 𝜑 is stable. Copy of notnotr 124 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
wl-notnotr (¬ ¬ 𝜑𝜑)

Proof of Theorem wl-notnotr
StepHypRef Expression
1 wl-id 32441 . 2 𝜑 → ¬ 𝜑)
21wl-con1i 32436 1 (¬ ¬ 𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 32417  ax-luk2 32418  ax-luk3 32419
This theorem is referenced by: (None)
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