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Theorem falxorfal 1490
Description: A  \/_ identity. (Contributed by David A. Wheeler, 9-May-2015.)
Assertion
Ref Expression
falxorfal  |-  ( ( F.  \/_ F.  )  <-> F.  )

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1401 . . 3  |-  ( ( F.  \/_ F.  )  <->  -.  ( F.  <-> F.  )
)
2 falbifal 1480 . . 3  |-  ( ( F.  <-> F.  )  <-> T.  )
31, 2xchbinx 311 . 2  |-  ( ( F.  \/_ F.  )  <->  -. T.  )
4 nottru 1473 . 2  |-  ( -. T.  <-> F.  )
53, 4bitri 252 1  |-  ( ( F.  \/_ F.  )  <-> F.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/_ wxo 1400   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-xor 1401  df-tru 1440  df-fal 1443
This theorem is referenced by: (None)
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