Theorem bj-0nmoore 37863

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 4284	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 37857	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 200	1 ⊢ ¬ ∅ ∈ Moore

This proof depends on syntax axioms:  ¬ wn 3   ∈ wcel 2145  ∅c0 4279  ∪ cuni 4867  Moorecmoore 37854

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732  ax-sep 5251  ax-nul 5263  ax-pow 5330

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-ral 3077  df-rex 3087  df-rab 3413  df-v 3452  df-dif 3902  df-in 3906  df-ss 3916  df-nul 4280  df-pw 4559  df-uni 4868  df-int 4908  df-bj-moore 37855

This theorem is used by:  bj-snmooreb  37865