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Theorem trunanfal 1345
Description: A  -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
trunanfal  |-  ( (  T.  -/\  F.  )  <->  T.  )

Proof of Theorem trunanfal
StepHypRef Expression
1 df-nan 1288 . 2  |-  ( (  T.  -/\  F.  )  <->  -.  (  T.  /\  F.  ) )
2 truanfal 1327 . . 3  |-  ( (  T.  /\  F.  )  <->  F.  )
32notbii 287 . 2  |-  ( -.  (  T.  /\  F.  ) 
<->  -.  F.  )
4 notfal 1339 . 2  |-  ( -. 
F. 
<->  T.  )
51, 3, 43bitri 262 1  |-  ( (  T.  -/\  F.  )  <->  T.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    /\ wa 358    -/\ wnan 1287    T. wtru 1307    F. wfal 1308
This theorem is referenced by:  falnantru  1346
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 177  df-an 360  df-nan 1288  df-tru 1310  df-fal 1311
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