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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,  _G |-  -.  -.  ps =>  _G |-  ps; see natded 25250. 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  |-  ( ph  ->  -.  -.  ps )
Assertion
Ref Expression
notnotrd  |-  ( ph  ->  ps )

Proof of Theorem notnotrd
StepHypRef Expression
1 notnotrd.1 . 2  |-  ( ph  ->  -.  -.  ps )
2 notnot2 112 . 2  |-  ( -. 
-.  ps  ->  ps )
31, 2syl 16 1  |-  ( ph  ->  ps )
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  794  efald  1417  necon1ai  2688  supgtoreq  7946  konigthlem  8960  indpi  9302  sqrmo  13096  ncoltgdim2  24077  ex-natded5.13  25262  2sqcoprm  27787  iccdifprioo  31717  icccncfext  31851  stirlinglem5  32021  bnj1204  34169
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