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Theorem falxorfal 1371
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 1315 . . 3  |-  ( (  F.  \/_  F.  )  <->  -.  (  F.  <->  F.  )
)
2 falbifal 1363 . . 3  |-  ( (  F.  <->  F.  )  <->  T.  )
31, 2xchbinx 303 . 2  |-  ( (  F.  \/_  F.  )  <->  -.  T.  )
4 nottru 1358 . 2  |-  ( -.  T.  <->  F.  )
53, 4bitri 242 1  |-  ( (  F.  \/_  F.  )  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    \/_ wxo 1314    T. wtru 1326    F. wfal 1327
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 179  df-xor 1315  df-tru 1329  df-fal 1330
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