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Theorem trunanfal 1482
Description: A  -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)
Assertion
Ref Expression
trunanfal  |-  ( ( T.  -/\ F.  )  <-> T.  )

Proof of Theorem trunanfal
StepHypRef Expression
1 df-nan 1380 . . 3  |-  ( ( T.  -/\ F.  )  <->  -.  ( T.  /\ F.  ) )
2 truanfal 1462 . . 3  |-  ( ( T.  /\ F.  )  <-> F.  )
31, 2xchbinx 311 . 2  |-  ( ( T.  -/\ F.  )  <->  -. F.  )
4 notfal 1474 . 2  |-  ( -. F.  <-> T.  )
53, 4bitri 252 1  |-  ( ( T.  -/\ F.  )  <-> T.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    /\ wa 370    -/\ wnan 1379   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-an 372  df-nan 1380  df-tru 1440  df-fal 1443
This theorem is referenced by:  falnantru  1484
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