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Theorem falxortru 1328
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
falxortru ((⊥ ⊻ ⊤) ↔ ⊤)

Proof of Theorem falxortru
StepHypRef Expression
1 df-xor 1283 . 2 ((⊥ ⊻ ⊤) ↔ ((⊥ ∨ ⊤) ∧ ¬ (⊥ ∧ ⊤)))
2 falortru 1314 . . 3 ((⊥ ∨ ⊤) ↔ ⊤)
3 notfal 1321 . . . 4 (¬ ⊥ ↔ ⊤)
4 falantru 1310 . . . 4 ((⊥ ∧ ⊤) ↔ ⊥)
53, 4xchnxbir 616 . . 3 (¬ (⊥ ∧ ⊤) ↔ ⊤)
62, 5anbi12i 441 . 2 (((⊥ ∨ ⊤) ∧ ¬ (⊥ ∧ ⊤)) ↔ (⊤ ∧ ⊤))
7 anidm 382 . 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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