Theorem bj-0nmoore 37774

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 4291	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 37768	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 200	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2143  ∅c0 4286  ∪ cuni 4872  Moorecmoore 37765

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5257  ax-nul 5269  ax-pow 5336

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ral 3080  df-rex 3090  df-rab 3417  df-v 3457  df-dif 3908  df-in 3912  df-ss 3922  df-nul 4287  df-pw 4564  df-uni 4873  df-int 4913  df-bj-moore 37766

This theorem is referenced by:  bj-snmooreb  37776