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Theorem bj-df-nul 33001
Description: Alternate definition of the empty class/set. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-df-nul ∅ = {𝑥 ∣ ⊥}

Proof of Theorem bj-df-nul
StepHypRef Expression
1 noel 3917 . . 3 ¬ 𝑥 ∈ ∅
21bifal 1496 . 2 (𝑥 ∈ ∅ ↔ ⊥)
32bj-abbi2i 32760 1 ∅ = {𝑥 ∣ ⊥}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1482  wfal 1487  wcel 1989  {cab 2607  c0 3913
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1485  df-fal 1488  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2752  df-v 3200  df-dif 3575  df-nul 3914
This theorem is referenced by: (None)
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