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Theorem bj-df-nul 34473
 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 4250 . . 3 ¬ 𝑥 ∈ ∅
21bifal 1554 . 2 (𝑥 ∈ ∅ ↔ ⊥)
32abbi2i 2932 1 ∅ = {𝑥 ∣ ⊥}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ⊥wfal 1550   ∈ wcel 2112  {cab 2779  ∅c0 4246 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-fal 1551  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-dif 3887  df-nul 4247 This theorem is referenced by: (None)
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