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Theorem falxorfal 1432
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 1386 . 2  |-  ( ( F.  \/_ F.  )  <->  ( ( F.  \/ F.  )  /\  -.  ( F. 
/\ F.  ) )
)
2 oridm 758 . . 3  |-  ( ( F.  \/ F.  )  <-> F.  )
3 notfal 1424 . . . 4  |-  ( -. F.  <-> T.  )
4 anidm 396 . . . 4  |-  ( ( F.  /\ F.  )  <-> F.  )
53, 4xchnxbir 682 . . 3  |-  ( -.  ( F.  /\ F.  ) 
<-> T.  )
62, 5anbi12i 460 . 2  |-  ( ( ( F.  \/ F.  )  /\  -.  ( F. 
/\ F.  ) )  <->  ( F.  /\ T.  ) )
7 falantru 1413 . 2  |-  ( ( F.  /\ T.  )  <-> F.  )
81, 6, 73bitri 206 1  |-  ( ( F.  \/_ F.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 104    <-> wb 105    \/ wo 709   T. wtru 1364   F. wfal 1368    \/_ wxo 1385
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-xor 1386
This theorem is referenced by: (None)
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