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Theorem falbitru 1380
Description: A  <-> identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
falbitru  |-  ( ( F.  <-> T.  )  <-> F.  )

Proof of Theorem falbitru
StepHypRef Expression
1 bicom 139 . 2  |-  ( ( F.  <-> T.  )  <->  ( T.  <-> F.  ) )
2 trubifal 1379 . 2  |-  ( ( T.  <-> F.  )  <-> F.  )
31, 2bitri 183 1  |-  ( ( F.  <-> T.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   T. wtru 1317   F. wfal 1321
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322
This theorem is referenced by: (None)
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