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

Theorem truxorfal 1426
Description: A  \/_ identity. (Contributed by David A. Wheeler, 8-May-2015.)
Assertion
Ref Expression
truxorfal  |-  ( ( T.  \/_ F.  )  <-> T.  )

Proof of Theorem truxorfal
StepHypRef Expression
1 df-xor 1361 . . 3  |-  ( ( T.  \/_ F.  )  <->  -.  ( T.  <-> F.  )
)
2 trubifal 1418 . . 3  |-  ( ( T.  <-> F.  )  <-> F.  )
31, 2xchbinx 310 . 2  |-  ( ( T.  \/_ F.  )  <->  -. F.  )
4 notfal 1416 . 2  |-  ( -. F.  <-> T.  )
53, 4bitri 249 1  |-  ( ( T.  \/_ F.  )  <-> T.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/_ wxo 1360   T. wtru 1380   F. wfal 1384
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 185  df-xor 1361  df-tru 1382  df-fal 1385
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator