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Theorem bifal 1487
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 1481 . 2 ¬ ⊥
31, 22false 363 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 194  wfal 1479
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 195  df-tru 1477  df-fal 1480
This theorem is referenced by:  falantru  1498  tgcgr4  25171  rusgra0edg  26275  frgrareg  26437  frgraregord013  26438  bj-df-nul  31991  bicontr  32832  aibnbaif  39506  aifftbifffaibif  39520  atnaiana  39522  ralnralall  40091  av-frgraregord013  41530
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