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Theorem falxortru 1427
Description: A  \/_ identity. (Contributed by David A. Wheeler, 9-May-2015.)
Assertion
Ref Expression
falxortru  |-  ( ( F.  \/_ T.  )  <-> T.  )

Proof of Theorem falxortru
StepHypRef Expression
1 df-xor 1361 . 2  |-  ( ( F.  \/_ T.  )  <->  -.  ( F.  <-> T.  )
)
2 falbitru 1419 . . 3  |-  ( ( F.  <-> T.  )  <-> F.  )
32notbii 296 . 2  |-  ( -.  ( F.  <-> T.  )  <->  -. F.  )
4 notfal 1416 . 2  |-  ( -. F.  <-> T.  )
51, 3, 43bitri 271 1  |-  ( ( F.  \/_ T.  )  <-> T.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1360   T. wtru 1380   F. wfal 1384
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 185  df-xor 1361  df-tru 1382  df-fal 1385
This theorem is referenced by: (None)
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