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Theorem truxortru 1398
 Description: A ⊻ identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxortru ((⊤ ⊻ ⊤) ↔ ⊥)

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1355 . 2 ((⊤ ⊻ ⊤) ↔ ((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)))
2 oridm 747 . . 3 ((⊤ ∨ ⊤) ↔ ⊤)
3 nottru 1392 . . . 4 (¬ ⊤ ↔ ⊥)
4 anidm 394 . . . 4 ((⊤ ∧ ⊤) ↔ ⊤)
53, 4xchnxbir 671 . . 3 (¬ (⊤ ∧ ⊤) ↔ ⊥)
62, 5anbi12i 456 . 2 (((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)) ↔ (⊤ ∧ ⊥))
7 truan 1349 . 2 ((⊤ ∧ ⊥) ↔ ⊥)
81, 6, 73bitri 205 1 ((⊤ ⊻ ⊤) ↔ ⊥)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 103   ↔ wb 104   ∨ wo 698  ⊤wtru 1333  ⊥wfal 1337   ⊻ wxo 1354 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-xor 1355 This theorem is referenced by: (None)
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