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Theorem falxorfal 1329
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
falxorfal ((⊥ ⊻ ⊥) ↔ ⊥)

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1283 . 2 ((⊥ ⊻ ⊥) ↔ ((⊥ ∨ ⊥) ∧ ¬ (⊥ ∧ ⊥)))
2 oridm 684 . . 3 ((⊥ ∨ ⊥) ↔ ⊥)
3 notfal 1321 . . . 4 (¬ ⊥ ↔ ⊤)
4 anidm 382 . . . 4 ((⊥ ∧ ⊥) ↔ ⊥)
53, 4xchnxbir 616 . . 3 (¬ (⊥ ∧ ⊥) ↔ ⊤)
62, 5anbi12i 441 . 2 (((⊥ ∨ ⊥) ∧ ¬ (⊥ ∧ ⊥)) ↔ (⊥ ∧ ⊤))
7 falantru 1310 . 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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