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Theorem notnot 136
Description: Double negation introduction. Converse of notnotr 125 and one implication of notnotb 304. Theorem *2.12 of [WhiteheadRussell] p. 101. This was the sixth axiom of Frege, specifically Proposition 41 of [Frege1879] p. 47. (Contributed by NM, 28-Dec-1992.) (Proof shortened by Wolf Lammen, 2-Mar-2013.)
Assertion
Ref Expression
notnot (𝜑 → ¬ ¬ 𝜑)

Proof of Theorem notnot
StepHypRef Expression
1 id 22 . 2 𝜑 → ¬ 𝜑)
21con2i 134 1 (𝜑 → ¬ ¬ 𝜑)
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:  notnoti  137  notnotd  138  con1d  139  con4iOLD  145  notnotb  304  biortn  421  pm2.13  434  nfntOLDOLD  1780  necon2ad  2805  necon4ad  2809  necon4ai  2821  eueq2  3367  ifnot  4111  knoppndvlem10  32207  wl-orel12  32965  cnfn1dd  33565  cnfn2dd  33566  axfrege41  37659  vk15.4j  38255  zfregs2VD  38598  vk15.4jVD  38672  con3ALTVD  38674  stoweidlem39  39593
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