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Theorem notnotrd 135
 Description: Deduction associated with notnotr 132 and notnotri 133. Double negation elimination rule. A translation of the natural deduction rule ¬ ¬ C , Γ⊢ ¬ ¬ 𝜓 ⇒ Γ⊢ 𝜓; see natded 28174. This is Definition NNC in [Pfenning] p. 17. This rule is valid in classical logic (our logic), but not in intuitionistic logic. (Contributed by DAW, 8-Feb-2017.)
Hypothesis
Ref Expression
notnotrd.1 (𝜑 → ¬ ¬ 𝜓)
Assertion
Ref Expression
notnotrd (𝜑𝜓)

Proof of Theorem notnotrd
StepHypRef Expression
1 notnotrd.1 . 2 (𝜑 → ¬ ¬ 𝜓)
2 notnotr 132 . 2 (¬ ¬ 𝜓𝜓)
31, 2syl 17 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem is referenced by:  condan  816  efald  1552  necon1ai  3041  supgtoreq  8926  konigthlem  9982  indpi  10321  sqrmo  14603  2sqcoprm  26003  axtgupdim2  26249  ncoltgdim2  26343  ex-natded5.13  28186  bnj1204  32277  knoppndvlem10  33853  supxrgere  41590  supxrgelem  41594  supxrge  41595  iccdifprioo  41781  icccncfext  42159  stirlinglem5  42353  sge0repnf  42658  sge0split  42681  nnfoctbdjlem  42727  nabctnabc  43157
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