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Theorem bifal 1557
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 1555 . 2 ¬ ⊥
31, 22false 375 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wfal 1553
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 1544  df-fal 1554
This theorem is referenced by:  falantru  1576  dfnul4  4282  dfnul2  4283  dfnul4OLD  4287  abf  4360  ralnralall  4474  tgcgr4  27302  frgrregord013  29168  nrmo  34820  bj-ntrufal  34971  bicontr  36477  aibnbaif  45043  aifftbifffaibif  45057  atnaiana  45059
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