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Theorem truxortru 1326
Description: A  \/_ identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxortru  |-  ( ( T.  \/_ T.  )  <-> F.  )

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1283 . 2  |-  ( ( T.  \/_ T.  )  <->  ( ( T.  \/ T.  )  /\  -.  ( T. 
/\ T.  ) ) )
2 oridm 684 . . 3  |-  ( ( T.  \/ T.  )  <-> T.  )
3 nottru 1320 . . . 4  |-  ( -. T.  <-> F.  )
4 anidm 382 . . . 4  |-  ( ( T.  /\ T.  )  <-> T.  )
53, 4xchnxbir 616 . . 3  |-  ( -.  ( T.  /\ T.  ) 
<-> F.  )
62, 5anbi12i 441 . 2  |-  ( ( ( T.  \/ T.  )  /\  -.  ( T. 
/\ T.  ) )  <-> 
( T.  /\ F.  ) )
7 truan 1276 . 2  |-  ( ( T.  /\ F.  )  <-> F.  )
81, 6, 73bitri 199 1  |-  ( ( T.  \/_ T.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 101    <-> wb 102    \/ wo 639   T. wtru 1260   F. wfal 1264    \/_ wxo 1282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-xor 1283
This theorem is referenced by: (None)
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