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Theorem notnot 142
Description: Double negation introduction. Converse of notnotr 130 and one implication of notnotb 315. 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 139 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  143  notnotd  144  con1d  145  notnotb  315  pm2.13  897  biortn  937  necon2ad  2955  necon4ad  2959  necon4ai  2972  eueq2  3669  ifnot  4539  spthcycl  33780  knoppndvlem10  35030  wl-orel12  36016  cnfn1dd  36597  cnfn2dd  36598  axfrege41  42204  vk15.4j  42898  zfregs2VD  43211  vk15.4jVD  43284  con3ALTVD  43286  stoweidlem39  44366
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