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Theorem falxorfal 1385
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
falxorfal ((⊥ ⊻ ⊥) ↔ ⊥)

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1339 . 2 ((⊥ ⊻ ⊥) ↔ ((⊥ ∨ ⊥) ∧ ¬ (⊥ ∧ ⊥)))
2 oridm 731 . . 3 ((⊥ ∨ ⊥) ↔ ⊥)
3 notfal 1377 . . . 4 (¬ ⊥ ↔ ⊤)
4 anidm 393 . . . 4 ((⊥ ∧ ⊥) ↔ ⊥)
53, 4xchnxbir 655 . . 3 (¬ (⊥ ∧ ⊥) ↔ ⊤)
62, 5anbi12i 455 . 2 (((⊥ ∨ ⊥) ∧ ¬ (⊥ ∧ ⊥)) ↔ (⊥ ∧ ⊤))
7 falantru 1366 . 2 ((⊥ ∧ ⊤) ↔ ⊥)
81, 6, 73bitri 205 1 ((⊥ ⊻ ⊥) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 103  wb 104  wo 682  wtru 1317  wfal 1321  wxo 1338
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 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-xor 1339
This theorem is referenced by: (None)
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