ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  truxortru Unicode version

Theorem truxortru 1356
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 1313 . 2  |-  ( ( T.  \/_ T.  )  <->  ( ( T.  \/ T.  )  /\  -.  ( T. 
/\ T.  ) ) )
2 oridm 710 . . 3  |-  ( ( T.  \/ T.  )  <-> T.  )
3 nottru 1350 . . . 4  |-  ( -. T.  <-> F.  )
4 anidm 389 . . . 4  |-  ( ( T.  /\ T.  )  <-> T.  )
53, 4xchnxbir 642 . . 3  |-  ( -.  ( T.  /\ T.  ) 
<-> F.  )
62, 5anbi12i 449 . 2  |-  ( ( ( T.  \/ T.  )  /\  -.  ( T. 
/\ T.  ) )  <-> 
( T.  /\ F.  ) )
7 truan 1307 . 2  |-  ( ( T.  /\ F.  )  <-> F.  )
81, 6, 73bitri 205 1  |-  ( ( T.  \/_ T.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    <-> wb 104    \/ wo 665   T. wtru 1291   F. wfal 1295    \/_ wxo 1312
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-fal 1296  df-xor 1313
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator