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Theorem bifal 1412
Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015.)
Hypothesis
Ref Expression
bifal.1  |-  -.  ph
Assertion
Ref Expression
bifal  |-  ( ph  <-> F.  )

Proof of Theorem bifal
StepHypRef Expression
1 bifal.1 . 2  |-  -.  ph
2 fal 1406 . 2  |-  -. F.
31, 22false 348 1  |-  ( ph  <-> F.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   F. wfal 1404
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 185  df-tru 1402  df-fal 1405
This theorem is referenced by:  falantru  1425  trubifalOLD  1440  rusgra0edg  25076  frgrareg  25238  frgraregord013  25239  bicontr  30643  aibnbaif  32268  ralnralall  32615  bj-df-nul  34932
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