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Theorem trunanfal 1364
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 1297 . 2  |-  ( (  T.  -/\  F.  )  <->  -.  (  T.  /\  F.  ) )
2 truanfal 1346 . . 3  |-  ( (  T.  /\  F.  )  <->  F.  )
32notbii 288 . 2  |-  ( -.  (  T.  /\  F.  ) 
<->  -.  F.  )
4 notfal 1358 . 2  |-  ( -. 
F. 
<->  T.  )
51, 3, 43bitri 263 1  |-  ( (  T.  -/\  F.  )  <->  T.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    /\ wa 359    -/\ wnan 1296    T. wtru 1325    F. wfal 1326
This theorem is referenced by:  falnantru  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-an 361  df-nan 1297  df-tru 1328  df-fal 1329
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