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Theorem bifal 1298
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 1292 . 2  |-  -. F.
31, 22false 650 1  |-  ( ph  <-> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103   F. wfal 1290
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291
This theorem is referenced by: (None)
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