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Theorem bifal 1488
 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 1482 . 2 ¬ ⊥
31, 22false 364 1 (𝜑 ↔ ⊥)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 195  ⊥wfal 1480 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 196  df-tru 1478  df-fal 1481 This theorem is referenced by:  falantru  1499  tgcgr4  25226  rusgra0edg  26482  frgrareg  26644  frgraregord013  26645  bj-df-nul  32208  bicontr  33049  aibnbaif  39723  aifftbifffaibif  39737  atnaiana  39739  ralnralall  40307  av-frgraregord013  41549
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