Theorem bj-0nmoore 37078

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 4360	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 37072	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 197	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2108  ∅c0 4352  ∪ cuni 4931  Moorecmoore 37069

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pow 5383

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ral 3068  df-rex 3077  df-rab 3444  df-v 3490  df-dif 3979  df-in 3983  df-ss 3993  df-nul 4353  df-pw 4624  df-uni 4932  df-int 4971  df-bj-moore 37070

This theorem is referenced by:  bj-snmooreb  37080