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Theorem notnot 138
Description: Double negation introduction. Converse of notnotr 128 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 136 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  139  notnotd  140  con1d  141  notnotb  304  pm2.13  863  biortn  897  nfntOLDOLD  1933  necon2ad  2957  necon4ad  2961  necon4ai  2973  eueq2  3530  ifnot  4270  knoppndvlem10  32843  wl-orel12  33624  cnfn1dd  34219  cnfn2dd  34220  axfrege41  38657  vk15.4j  39253  zfregs2VD  39592  vk15.4jVD  39666  con3ALTVD  39668  stoweidlem39  40767
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