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Theorem bifal 1318
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 1313 . 2  |-  -.  F.
31, 22false 339 1  |-  ( ph  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    F. wfal 1308
This theorem is referenced by:  truanfal  1327  falantru  1328  trubifal  1341  spfalw  1670  aibnbaif  27875
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-fal 1311
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