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Theorem trubifal 1477
Description: A  <-> identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)
Assertion
Ref Expression
trubifal  |-  ( ( T.  <-> F.  )  <-> F.  )

Proof of Theorem trubifal
StepHypRef Expression
1 bicom 203 . 2  |-  ( ( T.  <-> F.  )  <->  ( F.  <-> T.  ) )
2 falbitru 1476 . 2  |-  ( ( F.  <-> T.  )  <-> F.  )
31, 2bitri 252 1  |-  ( ( T.  <-> F.  )  <-> F.  )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 187   T. wtru 1438   F. wfal 1442
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 188  df-tru 1440
This theorem is referenced by:  falbitruOLD  1479  truxorfal  1487
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