Theorem bj-0nmoore 37602

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 4290	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 37596	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 199	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2142  ∅c0 4285  ∪ cuni 4865  Moorecmoore 37593

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734  ax-sep 5246  ax-nul 5256  ax-pow 5322

This theorem depends on definitions:  df-bi 209  df-an 400  df-3an 1100  df-tru 1563  df-fal 1573  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-ral 3077  df-rex 3087  df-rab 3415  df-v 3456  df-dif 3907  df-in 3911  df-ss 3921  df-nul 4286  df-pw 4557  df-uni 4866  df-int 4906  df-bj-moore 37594

This theorem is referenced by:  bj-snmooreb  37604