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Theorem falxorfal 1385
Description: A  \/_ identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
falxorfal  |-  ( ( F.  \/_ F.  )  <-> F.  )

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1339 . 2  |-  ( ( F.  \/_ F.  )  <->  ( ( F.  \/ F.  )  /\  -.  ( F. 
/\ F.  ) )
)
2 oridm 731 . . 3  |-  ( ( F.  \/ F.  )  <-> F.  )
3 notfal 1377 . . . 4  |-  ( -. F.  <-> T.  )
4 anidm 393 . . . 4  |-  ( ( F.  /\ F.  )  <-> F.  )
53, 4xchnxbir 655 . . 3  |-  ( -.  ( F.  /\ F.  ) 
<-> T.  )
62, 5anbi12i 455 . 2  |-  ( ( ( F.  \/ F.  )  /\  -.  ( F. 
/\ F.  ) )  <->  ( F.  /\ T.  ) )
7 falantru 1366 . 2  |-  ( ( F.  /\ T.  )  <-> F.  )
81, 6, 73bitri 205 1  |-  ( ( F.  \/_ F.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    <-> wb 104    \/ wo 682   T. wtru 1317   F. wfal 1321    \/_ wxo 1338
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-xor 1339
This theorem is referenced by: (None)
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