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Theorem truxortru 1430
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxortru ((⊤ ⊻ ⊤) ↔ ⊥)

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1387 . 2 ((⊤ ⊻ ⊤) ↔ ((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)))
2 oridm 758 . . 3 ((⊤ ∨ ⊤) ↔ ⊤)
3 nottru 1424 . . . 4 (¬ ⊤ ↔ ⊥)
4 anidm 396 . . . 4 ((⊤ ∧ ⊤) ↔ ⊤)
53, 4xchnxbir 682 . . 3 (¬ (⊤ ∧ ⊤) ↔ ⊥)
62, 5anbi12i 460 . 2 (((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)) ↔ (⊤ ∧ ⊥))
7 truan 1381 . 2 ((⊤ ∧ ⊥) ↔ ⊥)
81, 6, 73bitri 206 1 ((⊤ ⊻ ⊤) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 104  wb 105  wo 709  wtru 1365  wfal 1369  wxo 1386
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-xor 1387
This theorem is referenced by: (None)
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