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Theorem trunanfal 1522
 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 1445 . . 3 ((⊤ ⊼ ⊥) ↔ ¬ (⊤ ∧ ⊥))
2 truanfal 1504 . . 3 ((⊤ ∧ ⊥) ↔ ⊥)
31, 2xchbinx 324 . 2 ((⊤ ⊼ ⊥) ↔ ¬ ⊥)
4 notfal 1516 . 2 (¬ ⊥ ↔ ⊤)
53, 4bitri 264 1 ((⊤ ⊼ ⊥) ↔ ⊤)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 196   ∧ wa 384   ⊼ wnan 1444  ⊤wtru 1481  ⊥wfal 1485 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 386  df-nan 1445  df-tru 1483  df-fal 1486 This theorem is referenced by:  falnantru  1523
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