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Theorem falxorfal 1361
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 1305 . . 3  |-  ( (  F.  \/_  F.  )  <->  -.  (  F.  <->  F.  )
)
2 falbifal 1353 . . 3  |-  ( (  F.  <->  F.  )  <->  T.  )
31, 2xchbinx 301 . 2  |-  ( (  F.  \/_  F.  )  <->  -.  T.  )
4 nottru 1348 . 2  |-  ( -.  T.  <->  F.  )
53, 4bitri 240 1  |-  ( (  F.  \/_  F.  )  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/_ wxo 1304    T. wtru 1316    F. wfal 1317
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 177  df-xor 1305  df-tru 1319  df-fal 1320
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