Theorem bj-0nmoore 35981

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

Step	Hyp	Ref	Expression
1		noel 4329	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 35975	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 196	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2106  ∅c0 4321  ∪ cuni 4907  Moorecmoore 35972

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-sep 5298  ax-nul 5305  ax-pow 5362

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3950  df-in 3954  df-ss 3964  df-nul 4322  df-pw 4603  df-uni 4908  df-int 4950  df-bj-moore 35973

This theorem is referenced by:  bj-snmooreb  35983