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Theorem falbitru 1349
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 138 . 2  |-  ( ( F.  <-> T.  )  <->  ( T.  <-> F.  ) )
2 trubifal 1348 . 2  |-  ( ( T.  <-> F.  )  <-> F.  )
31, 2bitri 182 1  |-  ( ( F.  <-> T.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:    <-> wb 103   T. wtru 1286   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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