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Theorem notnotrd 105
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 20806. 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 104 . 2  |-  ( -. 
-.  ps  ->  ps )
31, 2syl 15 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  efald  1324  sqrmo  11753  ex-natded5.13  20818  stirlinglem5  27930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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