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Theorem notnotrd 113
Description: Deduction converting double-negation into the original wff, aka the double negation rule. A translation of natural deduction rule -.-. -C, |--.-. => |- ; see natded 25124. This is definition NNC in [Pfenning] p. 17. This rule is valid in classical logic (which MPE uses), but not intuitionistic logic. (Contributed by DAW, 8-Feb-2017.)
Hypothesis
Ref Expression
notnotrd.1
Assertion
Ref Expression
notnotrd

Proof of Theorem notnotrd
StepHypRef Expression
1 notnotrd.1 . 2
2 notnot2 112 . 2
31, 2syl 16 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4
This theorem is referenced by:  condan  794  efald  1417  necon1ai  2688  supgtoreq  7949  konigthlem  8964  indpi  9306  sqrmo  13085  ncoltgdim2  23952  ex-natded5.13  25136  2sqcoprm  27635  iccdifprioo  31556  icccncfext  31690  stirlinglem5  31860  bnj1204  34068
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
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