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Theorem nbfal 1327
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 1323 . 2 ¬ ⊥
21nbn 673 1 𝜑 ↔ (𝜑 ↔ ⊥))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104  wfal 1321
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322
This theorem is referenced by:  zfnuleu  4022
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