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Theorem bj-0nmoore 33373
 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 4062 . 2 ¬ ∅ ∈ ∅
2 bj-ismoored0 33367 . 2 (∅ ∈ Moore ∅ ∈ ∅)
31, 2mto 188 1 ¬ ∅ ∈ Moore
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∈ wcel 2139  ∅c0 4058  ∪ cuni 4588  Moorecmoore 33363 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-nul 4941 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ral 3055  df-rex 3056  df-v 3342  df-dif 3718  df-in 3722  df-ss 3729  df-nul 4059  df-pw 4304  df-uni 4589  df-int 4628  df-bj-moore 33364 This theorem is referenced by:  bj-snmoore  33374
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