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Theorem bifal 1345
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 1339 . 2 ¬ ⊥
31, 22false 691 1 (𝜑 ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104  wfal 1337
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338
This theorem is referenced by: (None)
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