Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  notnotrd Structured version   Unicode version

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 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
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 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
 Copyright terms: Public domain W3C validator