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Theorem notnot1 122
Description: Converse of double negation. 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
notnot1  |-  ( ph  ->  -.  -.  ph )

Proof of Theorem notnot1
StepHypRef Expression
1 id 22 . 2  |-  ( -. 
ph  ->  -.  ph )
21con2i 120 1  |-  ( ph  ->  -.  -.  ph )
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  123  con1d  124  con4i  130  notnot  291  biortn  406  pm2.13  418  necon2ad  2670  necon4ad  2677  necon4ai  2695  eueq2  3273  ifnot  3989  nbusgra  24554  wlkntrl  24690  eupath2  25106  cnfn1dd  30654  cnfn2dd  30655  stoweidlem39  31982  vk15.4j  33399  zfregs2VD  33742  vk15.4jVD  33815  con3ALTVD  33817  axfrege41  37972
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