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Theorem falxorfal 1367
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 1311 . . 3  |-  ( (  F.  \/_  F.  )  <->  -.  (  F.  <->  F.  )
)
2 falbifal 1359 . . 3  |-  ( (  F.  <->  F.  )  <->  T.  )
31, 2xchbinx 302 . 2  |-  ( (  F.  \/_  F.  )  <->  -.  T.  )
4 nottru 1354 . 2  |-  ( -.  T.  <->  F.  )
53, 4bitri 241 1  |-  ( (  F.  \/_  F.  )  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/_ wxo 1310    T. wtru 1322    F. wfal 1323
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-xor 1311  df-tru 1325  df-fal 1326
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