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Theorem nbfal 1644
Description: The negation of a proposition is equivalent to itself being equivalent to . (Contributed by Anthony Hart, 14-Aug-2011.)
Assertion
Ref Expression
nbfal 𝜑 ↔ (𝜑 ↔ ⊥))

Proof of Theorem nbfal
StepHypRef Expression
1 fal 1639 . 2 ¬ ⊥
21nbn 361 1 𝜑 ↔ (𝜑 ↔ ⊥))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wfal 1637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-tru 1635  df-fal 1638
This theorem is referenced by:  zfnuleu  4938  bisym1  32724  aisfina  41571  aifftbifffaibifff  41595  lindslinindsimp2  42762
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