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Theorem trunanfal 1565
Description: A identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)
Assertion
Ref Expression
trunanfal ((⊤ ⊼ ⊥) ↔ ⊤)

Proof of Theorem trunanfal
StepHypRef Expression
1 df-nan 1488 . . 3 ((⊤ ⊼ ⊥) ↔ ¬ (⊤ ∧ ⊥))
2 truanfal 1547 . . 3 ((⊤ ∧ ⊥) ↔ ⊥)
31, 2xchbinx 323 . 2 ((⊤ ⊼ ⊥) ↔ ¬ ⊥)
4 notfal 1559 . 2 (¬ ⊥ ↔ ⊤)
53, 4bitri 264 1 ((⊤ ⊼ ⊥) ↔ ⊤)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 383  wnan 1487  wtru 1524  wfal 1528
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 197  df-an 385  df-nan 1488  df-tru 1526  df-fal 1529
This theorem is referenced by:  falnantru  1566
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