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Theorem notnotrd 133
Description: Deduction associated with notnotr 130 and notnotri 131. Double negation elimination rule. A translation of the natural deduction rule ¬ ¬ C , Γ¬ ¬ 𝜓 ⇒ Γ𝜓; see natded 28767. 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 130 . 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  815  ecase2d  1027  efald  1560  necon1ai  2971  supgtoreq  9229  konigthlem  10324  indpi  10663  sqrmo  14963  2sqcoprm  26583  axtgupdim2  26832  ncoltgdim2  26926  ex-natded5.13  28779  bnj1204  32992  knoppndvlem10  34701  supxrgere  42872  supxrgelem  42876  supxrge  42877  iccdifprioo  43054  icccncfext  43428  stirlinglem5  43619  sge0repnf  43924  sge0split  43947  nnfoctbdjlem  43993  nabctnabc  44426
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