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Theorem truxorfal 1311
Description: A  \/_ identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxorfal  |-  ( ( T.  \/_ F.  )  <-> T.  )

Proof of Theorem truxorfal
StepHypRef Expression
1 df-xor 1267 . 2  |-  ( ( T.  \/_ F.  )  <->  ( ( T.  \/ F.  )  /\  -.  ( T. 
/\ F.  ) )
)
2 truorfal 1297 . . 3  |-  ( ( T.  \/ F.  )  <-> T.  )
3 notfal 1305 . . . 4  |-  ( -. F.  <-> T.  )
4 truan 1260 . . . 4  |-  ( ( T.  /\ F.  )  <-> F.  )
53, 4xchnxbir 606 . . 3  |-  ( -.  ( T.  /\ F.  ) 
<-> T.  )
62, 5anbi12i 433 . 2  |-  ( ( ( T.  \/ F.  )  /\  -.  ( T. 
/\ F.  ) )  <->  ( T.  /\ T.  ) )
7 anidm 376 . 2  |-  ( ( T.  /\ T.  )  <-> T.  )
81, 6, 73bitri 195 1  |-  ( ( T.  \/_ F.  )  <-> T.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 97    <-> wb 98    \/ wo 629   T. wtru 1244   F. wfal 1248    \/_ wxo 1266
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-xor 1267
This theorem is referenced by: (None)
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