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Theorem bifal 1553
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 1551 . 2 ¬ ⊥
31, 22false 375 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 206  wfal 1549
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 1540  df-fal 1550
This theorem is referenced by:  falantru  1572  dfnul4  4354  dfnul2  4355  dfnul4OLD  4359  abf  4429  ralnralall  4538  tgcgr4  28557  frgrregord013  30427  nrmo  36376  bj-ntrufal  36535  bicontr  38040  aibnbaif  46822  aifftbifffaibif  46836  atnaiana  46838
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