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Theorem bj-0nmoore 34527
 Description: The empty set is not a Moore collection. (Contributed by BJ, 9-Dec-2021.)
Assertion
Ref Expression
bj-0nmoore ¬ ∅ ∈ Moore

Proof of Theorem bj-0nmoore
StepHypRef Expression
1 noel 4247 . 2 ¬ ∅ ∈ ∅
2 bj-ismoored0 34521 . 2 (∅ ∈ Moore ∅ ∈ ∅)
31, 2mto 200 1 ¬ ∅ ∈ Moore
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2111  ∅c0 4243  ∪ cuni 4800  Moorecmoore 34518 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 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5167  ax-nul 5174  ax-pow 5231 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rab 3115  df-v 3443  df-dif 3884  df-in 3888  df-ss 3898  df-nul 4244  df-pw 4499  df-uni 4801  df-int 4839  df-bj-moore 34519 This theorem is referenced by:  bj-snmooreb  34529
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