MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  falxorfal Structured version   Visualization version   Unicode version

Theorem falxorfal 1503
Description: A  \/_ identity. (Contributed by David A. Wheeler, 9-May-2015.)
Assertion
Ref Expression
falxorfal  |-  ( ( F.  \/_ F.  )  <-> F.  )

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1431 . . 3  |-  ( ( F.  \/_ F.  )  <->  -.  ( F.  <-> F.  )
)
2 falbifal 1493 . . 3  |-  ( ( F.  <-> F.  )  <-> T.  )
31, 2xchbinx 317 . 2  |-  ( ( F.  \/_ F.  )  <->  -. T.  )
4 nottru 1486 . 2  |-  ( -. T.  <-> F.  )
53, 4bitri 257 1  |-  ( ( F.  \/_ F.  )  <-> F.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 189    \/_ wxo 1430   T. wtru 1453   F. wfal 1457
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 190  df-xor 1431  df-tru 1455  df-fal 1458
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator