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Theorem nbfal 1270
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 1266 . 2 ¬ ⊥
21nbn 625 1 𝜑 ↔ (𝜑 ↔ ⊥))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102  wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  zfnuleu  3908
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