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Theorem trunanfal 1355
Description: A identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
trunanfal (( ⊤ ⊥ ) ↔ ⊤ )

Proof of Theorem trunanfal
StepHypRef Expression
1 df-nan 1288 . 2 (( ⊤ ⊥ ) ↔ ¬ ( ⊤ ⊥ ))
2 truanfal 1337 . . 3 (( ⊤ ⊥ ) ↔ ⊥ )
32notbii 287 . 2 (¬ ( ⊤ ⊥ ) ↔ ¬ ⊥ )
4 notfal 1349 . 2 (¬ ⊥ ↔ ⊤ )
51, 3, 43bitri 262 1 (( ⊤ ⊥ ) ↔ ⊤ )
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   wa 358   wnan 1287  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-an 360  df-nan 1288  df-tru 1319  df-fal 1320
This theorem is referenced by:  falnantru  1356
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