Theorem bj-0nmoore 37113

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 4338	. 2 ⊢ ¬ ∪ ∅ ∈ ∅
2		bj-ismoored0 37107	. 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅)
3	1, 2	mto 197	1 ⊢ ¬ ∅ ∈ Moore

Syntax hints:  ¬ wn 3   ∈ wcel 2108  ∅c0 4333  ∪ cuni 4907  Moorecmoore 37104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pow 5365

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-in 3958  df-ss 3968  df-nul 4334  df-pw 4602  df-uni 4908  df-int 4947  df-bj-moore 37105

This theorem is referenced by:  bj-snmooreb  37115