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Theorem bifal 1272
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 1266 . 2 ¬ ⊥
31, 22false 627 1 (𝜑 ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 102  wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by: (None)
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