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Theorem falxorfal 1701
Description: A identity. (Contributed by David A. Wheeler, 9-May-2015.)
Assertion
Ref Expression
falxorfal ((⊥ ⊻ ⊥) ↔ ⊥)

Proof of Theorem falxorfal
StepHypRef Expression
1 df-xor 1634 . . 3 ((⊥ ⊻ ⊥) ↔ ¬ (⊥ ↔ ⊥))
2 falbifal 1685 . . 3 ((⊥ ↔ ⊥) ↔ ⊤)
31, 2xchbinx 325 . 2 ((⊥ ⊻ ⊥) ↔ ¬ ⊤)
4 nottru 1680 . 2 (¬ ⊤ ↔ ⊥)
53, 4bitri 266 1 ((⊥ ⊻ ⊥) ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 197  wxo 1633  wtru 1653  wfal 1665
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-xor 1634  df-tru 1656  df-fal 1666
This theorem is referenced by: (None)
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