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Theorem bifal 1383
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 1377 . 2  |-  -. F.
31, 22false 350 1  |-  ( ph  <-> F.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   F. wfal 1375
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 1373  df-fal 1376
This theorem is referenced by:  falantru  1396  trubifal  1409  bicontr  29020  aibnbaif  30061  ralnralall  30258  rusgra0edg  30713  frgrareg  30850  frgraregord013  30851  bj-df-nul  32821
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