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Theorem falxorfal 1354
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 1308 . 2  |-  ( ( F.  \/_ F.  )  <->  ( ( F.  \/ F.  )  /\  -.  ( F. 
/\ F.  ) )
)
2 oridm 707 . . 3  |-  ( ( F.  \/ F.  )  <-> F.  )
3 notfal 1346 . . . 4  |-  ( -. F.  <-> T.  )
4 anidm 388 . . . 4  |-  ( ( F.  /\ F.  )  <-> F.  )
53, 4xchnxbir 639 . . 3  |-  ( -.  ( F.  /\ F.  ) 
<-> T.  )
62, 5anbi12i 448 . 2  |-  ( ( ( F.  \/ F.  )  /\  -.  ( F. 
/\ F.  ) )  <->  ( F.  /\ T.  ) )
7 falantru 1335 . 2  |-  ( ( F.  /\ T.  )  <-> F.  )
81, 6, 73bitri 204 1  |-  ( ( F.  \/_ F.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 102    <-> wb 103    \/ wo 662   T. wtru 1286   F. wfal 1290    \/_ wxo 1307
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-xor 1308
This theorem is referenced by: (None)
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