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Theorem bifal 1556
Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015.)
Hypothesis
Ref Expression
bifal.1 ¬ 𝜑
Assertion
Ref Expression
bifal (𝜑 ↔ ⊥)

Proof of Theorem bifal
StepHypRef Expression
1 bifal.1 . 2 ¬ 𝜑
2 fal 1554 . 2 ¬ ⊥
31, 22false 375 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 206  wfal 1552
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 207  df-tru 1543  df-fal 1553
This theorem is referenced by:  falantru  1575  dfnul4  4335  dfnul2  4336  abf  4406  ralnralall  4515  tgcgr4  28539  frgrregord013  30414  nrmo  36411  bj-ntrufal  36570  bicontr  38087  aibnbaif  46919  aifftbifffaibif  46933  atnaiana  46935
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