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Theorem nbfal 1557
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 1556 . 2 ¬ ⊥
21nbn 373 1 𝜑 ↔ (𝜑 ↔ ⊥))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wfal 1554
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 206  df-tru 1545  df-fal 1555
This theorem is referenced by:  nulmo  2709  eq0  4304  ab0  4335  ab0OLD  4336  eq0rdv  4365  rzal  4467  bisym1  34937  wl-1xor  35999  wl-1mintru1  36005  aisfina  45219  aifftbifffaibifff  45243  lindslinindsimp2  46630
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