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Theorem trubifal 1323
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 374 . 2  |-  ( ( T.  <-> F.  )  <->  ( ( T.  -> F.  )  /\  ( F.  -> T.  ) ) )
2 truimfal 1317 . . 3  |-  ( ( T.  -> F.  )  <-> F.  )
3 falimtru 1318 . . 3  |-  ( ( F.  -> T.  )  <-> T.  )
42, 3anbi12i 441 . 2  |-  ( ( ( T.  -> F.  )  /\  ( F.  -> T.  ) )  <->  ( F.  /\ T.  ) )
5 falantru 1310 . 2  |-  ( ( F.  /\ T.  )  <-> F.  )
61, 4, 53bitri 199 1  |-  ( ( T.  <-> F.  )  <-> F.  )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    <-> wb 102   T. wtru 1260   F. wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  falbitru  1324
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