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Theorem falxortru 1382
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
falxortru ((⊥ ⊻ ⊤) ↔ ⊤)

Proof of Theorem falxortru
StepHypRef Expression
1 df-xor 1337 . 2 ((⊥ ⊻ ⊤) ↔ ((⊥ ∨ ⊤) ∧ ¬ (⊥ ∧ ⊤)))
2 falortru 1368 . . 3 ((⊥ ∨ ⊤) ↔ ⊤)
3 notfal 1375 . . . 4 (¬ ⊥ ↔ ⊤)
4 falantru 1364 . . . 4 ((⊥ ∧ ⊤) ↔ ⊥)
53, 4xchnxbir 653 . . 3 (¬ (⊥ ∧ ⊤) ↔ ⊤)
62, 5anbi12i 453 . 2 (((⊥ ∨ ⊤) ∧ ¬ (⊥ ∧ ⊤)) ↔ (⊤ ∧ ⊤))
7 anidm 391 . 2 ((⊤ ∧ ⊤) ↔ ⊤)
81, 6, 73bitri 205 1 ((⊥ ⊻ ⊤) ↔ ⊤)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 103  wb 104  wo 680  wtru 1315  wfal 1319  wxo 1336
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 586  ax-in2 587  ax-io 681
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-xor 1337
This theorem is referenced by: (None)
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