Theorem bj-0nmoore 35210

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 4261	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 35204	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 196	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2108  ∅c0 4253  ∪ cuni 4836  Moorecmoore 35201

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pow 5283

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-ral 3068  df-rab 3072  df-v 3424  df-dif 3886  df-in 3890  df-ss 3900  df-nul 4254  df-pw 4532  df-uni 4837  df-int 4877  df-bj-moore 35202

This theorem is referenced by:  bj-snmooreb  35212