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Theorem truxortru 1365
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
truxortru ((⊤ ⊻ ⊤) ↔ ⊥)

Proof of Theorem truxortru
StepHypRef Expression
1 df-xor 1322 . 2 ((⊤ ⊻ ⊤) ↔ ((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)))
2 oridm 715 . . 3 ((⊤ ∨ ⊤) ↔ ⊤)
3 nottru 1359 . . . 4 (¬ ⊤ ↔ ⊥)
4 anidm 391 . . . 4 ((⊤ ∧ ⊤) ↔ ⊤)
53, 4xchnxbir 647 . . 3 (¬ (⊤ ∧ ⊤) ↔ ⊥)
62, 5anbi12i 451 . 2 (((⊤ ∨ ⊤) ∧ ¬ (⊤ ∧ ⊤)) ↔ (⊤ ∧ ⊥))
7 truan 1316 . 2 ((⊤ ∧ ⊥) ↔ ⊥)
81, 6, 73bitri 205 1 ((⊤ ⊻ ⊤) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 103  wb 104  wo 670  wtru 1300  wfal 1304  wxo 1321
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-fal 1305  df-xor 1322
This theorem is referenced by: (None)
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