Theorem bj-0nmoore 34975

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 4235	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 34969	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 200	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2110  ∅c0 4227  ∪ cuni 4809  Moorecmoore 34966

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2706  ax-sep 5181  ax-nul 5188  ax-pow 5247

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2713  df-cleq 2726  df-clel 2812  df-ral 3059  df-rab 3063  df-v 3403  df-dif 3860  df-in 3864  df-ss 3874  df-nul 4228  df-pw 4505  df-uni 4810  df-int 4850  df-bj-moore 34967

This theorem is referenced by:  bj-snmooreb  34977