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Theorem truxorfal 1402
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 1358 . 2  |-  ( ( T.  \/_ F.  )  <->  ( ( T.  \/ F.  )  /\  -.  ( T. 
/\ F.  ) )
)
2 truorfal 1388 . . 3  |-  ( ( T.  \/ F.  )  <-> T.  )
3 notfal 1396 . . . 4  |-  ( -. F.  <-> T.  )
4 truan 1352 . . . 4  |-  ( ( T.  /\ F.  )  <-> F.  )
53, 4xchnxbir 671 . . 3  |-  ( -.  ( T.  /\ F.  ) 
<-> T.  )
62, 5anbi12i 456 . 2  |-  ( ( ( T.  \/ F.  )  /\  -.  ( T. 
/\ F.  ) )  <->  ( T.  /\ T.  ) )
7 anidm 394 . 2  |-  ( ( T.  /\ T.  )  <-> T.  )
81, 6, 73bitri 205 1  |-  ( ( T.  \/_ F.  )  <-> T.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    <-> wb 104    \/ wo 698   T. wtru 1336   F. wfal 1340    \/_ wxo 1357
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 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341  df-xor 1358
This theorem is referenced by: (None)
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