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Theorem truxortru 1568
Description: A identity. (Contributed by David A. Wheeler, 8-May-2015.)
Assertion
Ref Expression
truxortru ((⊤ ⊻ ⊤) ↔ ⊥)

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1505 . . 3 ((⊤ ⊻ ⊤) ↔ ¬ (⊤ ↔ ⊤))
2 trubitru 1560 . . 3 ((⊤ ↔ ⊤) ↔ ⊤)
31, 2xchbinx 323 . 2 ((⊤ ⊻ ⊤) ↔ ¬ ⊤)
4 nottru 1558 . 2 (¬ ⊤ ↔ ⊥)
53, 4bitri 264 1 ((⊤ ⊻ ⊤) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wxo 1504  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-xor 1505  df-tru 1526  df-fal 1529
This theorem is referenced by: (None)
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