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Theorem trubifal 1357
Description: A  <-> identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
trubifal  |-  ( (  T.  <->  F.  )  <->  F.  )

Proof of Theorem trubifal
StepHypRef Expression
1 nottru 1354 . . 3  |-  ( -.  T.  <->  F.  )
2 nbbn 348 . . 3  |-  ( ( -.  T.  <->  F.  )  <->  -.  (  T.  <->  F.  )
)
31, 2mpbi 200 . 2  |-  -.  (  T. 
<->  F.  )
43bifal 1333 1  |-  ( (  T.  <->  F.  )  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    T. wtru 1322    F. wfal 1323
This theorem is referenced by:  falbitru  1358  truxorfal  1365
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 178  df-tru 1325  df-fal 1326
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