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Theorem trubifal 1379
Description: A  <-> identity. (Contributed by David A. Wheeler, 23-Feb-2018.)
Assertion
Ref Expression
trubifal  |-  ( ( T.  <-> F.  )  <-> F.  )

Proof of Theorem trubifal
StepHypRef Expression
1 dfbi2 385 . 2  |-  ( ( T.  <-> F.  )  <->  ( ( T.  -> F.  )  /\  ( F.  -> T.  ) ) )
2 truimfal 1373 . . 3  |-  ( ( T.  -> F.  )  <-> F.  )
3 falimtru 1374 . . 3  |-  ( ( F.  -> T.  )  <-> T.  )
42, 3anbi12i 455 . 2  |-  ( ( ( T.  -> F.  )  /\  ( F.  -> T.  ) )  <->  ( F.  /\ T.  ) )
5 falantru 1366 . 2  |-  ( ( F.  /\ T.  )  <-> F.  )
61, 4, 53bitri 205 1  |-  ( ( T.  <-> F.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104   T. wtru 1317   F. wfal 1321
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 588  ax-in2 589
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322
This theorem is referenced by:  falbitru  1380
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