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

Proof of Theorem truxorfal
StepHypRef Expression
1 df-xor 1386 . 2 ((⊤ ⊻ ⊥) ↔ ((⊤ ∨ ⊥) ∧ ¬ (⊤ ∧ ⊥)))
2 truorfal 1416 . . 3 ((⊤ ∨ ⊥) ↔ ⊤)
3 notfal 1424 . . . 4 (¬ ⊥ ↔ ⊤)
4 truan 1380 . . . 4 ((⊤ ∧ ⊥) ↔ ⊥)
53, 4xchnxbir 682 . . 3 (¬ (⊤ ∧ ⊥) ↔ ⊤)
62, 5anbi12i 460 . 2 (((⊤ ∨ ⊥) ∧ ¬ (⊤ ∧ ⊥)) ↔ (⊤ ∧ ⊤))
7 anidm 396 . 2 ((⊤ ∧ ⊤) ↔ ⊤)
81, 6, 73bitri 206 1 ((⊤ ⊻ ⊥) ↔ ⊤)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 104  wb 105  wo 709  wtru 1364  wfal 1368  wxo 1385
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 1366  df-fal 1369  df-xor 1386
This theorem is referenced by: (None)
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