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Theorem notnotrd 127
Description: Deduction associated with notnotr 124 and notnotri 125. Double negation elimination rule. A translation of the natural deduction rule ¬ ¬ C , Γ¬ ¬ 𝜓 ⇒ Γ𝜓; see natded 26652. 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 124 . 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  831  efald  1495  necon1ai  2809  supgtoreq  8259  konigthlem  9269  indpi  9608  sqrmo  13840  axtgupdim2  25170  ncoltgdim2  25260  ex-natded5.13  26664  2sqcoprm  28978  bnj1204  30334  knoppndvlem10  31682  supxrgere  38490  supxrgelem  38494  supxrge  38495  iccdifprioo  38589  icccncfext  38773  stirlinglem5  38971  sge0repnf  39279  sge0split  39302  nnfoctbdjlem  39348  nabctnabc  39747
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