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Theorem truxortru 1573
Description: A identity. (Contributed by David A. Wheeler, 8-May-2015.)
Assertion
Ref Expression
truxortru ((⊤ ⊻ ⊤) ↔ ⊥)

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1496 . . 3 ((⊤ ⊻ ⊤) ↔ ¬ (⊤ ↔ ⊤))
2 trubitru 1557 . . 3 ((⊤ ↔ ⊤) ↔ ⊤)
31, 2xchbinx 335 . 2 ((⊤ ⊻ ⊤) ↔ ¬ ⊤)
4 nottru 1555 . 2 (¬ ⊤ ↔ ⊥)
53, 4bitri 276 1 ((⊤ ⊻ ⊤) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 207  wxo 1495  wtru 1529  wfal 1540
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 208  df-xor 1496  df-tru 1531  df-fal 1541
This theorem is referenced by: (None)
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