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Theorem trubifal 1351
Description: A identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
trubifal (( ⊤ ↔ ⊥ ) ↔ ⊥ )

Proof of Theorem trubifal
StepHypRef Expression
1 nottru 1348 . . 3 (¬ ⊤ ↔ ⊥ )
2 nbbn 347 . . 3 ((¬ ⊤ ↔ ⊥ ) ↔ ¬ ( ⊤ ↔ ⊥ ))
31, 2mpbi 199 . 2 ¬ ( ⊤ ↔ ⊥ )
43bifal 1327 1 (( ⊤ ↔ ⊥ ) ↔ ⊥ )
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176  wtru 1316  wfal 1317
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 177  df-tru 1319  df-fal 1320
This theorem is referenced by:  falbitru  1352  truxorfal  1359
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