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Theorem truxortru 1326
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxortru ((⊤ ⊻ ⊤) ↔ ⊥)

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1283 . 2 ((⊤ ⊻ ⊤) ↔ ((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)))
2 oridm 684 . . 3 ((⊤ ∨ ⊤) ↔ ⊤)
3 nottru 1320 . . . 4 (¬ ⊤ ↔ ⊥)
4 anidm 382 . . . 4 ((⊤ ∧ ⊤) ↔ ⊤)
53, 4xchnxbir 616 . . 3 (¬ (⊤ ∧ ⊤) ↔ ⊥)
62, 5anbi12i 441 . 2 (((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)) ↔ (⊤ ∧ ⊥))
7 truan 1276 . 2 ((⊤ ∧ ⊥) ↔ ⊥)
81, 6, 73bitri 199 1 ((⊤ ⊻ ⊤) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 101  wb 102  wo 639  wtru 1260  wfal 1264  wxo 1282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-xor 1283
This theorem is referenced by: (None)
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