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Theorem notnot 144
Description: Double negation introduction. Converse of notnotr 132 and one implication of notnotb 316. 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 141 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  145  notnotd  146  con1d  147  notnotb  316  pm2.13  891  biortn  931  necon2ad  3028  necon4ad  3032  necon4ai  3044  eueq2  3698  ifnot  4513  spthcycl  32273  knoppndvlem10  33757  wl-orel12  34633  cnfn1dd  35251  cnfn2dd  35252  axfrege41  40068  vk15.4j  40739  zfregs2VD  41052  vk15.4jVD  41125  con3ALTVD  41127  stoweidlem39  42201
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