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Theorem falxorfal 1313
Description: A identity. (Contributed by David A. Wheeler, 2-Mar-2018.)
Assertion
Ref Expression
falxorfal ((⊥ ⊻ ⊥) ↔ ⊥)

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1267 . 2 ((⊥ ⊻ ⊥) ↔ ((⊥ ∨ ⊥) ∧ ¬ (⊥ ∧ ⊥)))
2 oridm 674 . . 3 ((⊥ ∨ ⊥) ↔ ⊥)
3 notfal 1305 . . . 4 (¬ ⊥ ↔ ⊤)
4 anidm 376 . . . 4 ((⊥ ∧ ⊥) ↔ ⊥)
53, 4xchnxbir 606 . . 3 (¬ (⊥ ∧ ⊥) ↔ ⊤)
62, 5anbi12i 433 . 2 (((⊥ ∨ ⊥) ∧ ¬ (⊥ ∧ ⊥)) ↔ (⊥ ∧ ⊤))
7 falantru 1294 . 2 ((⊥ ∧ ⊤) ↔ ⊥)
81, 6, 73bitri 195 1 ((⊥ ⊻ ⊥) ↔ ⊥)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 97  wb 98  wo 629  wtru 1244  wfal 1248  wxo 1266
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-xor 1267
This theorem is referenced by: (None)
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