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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-0nmoore | Structured version Visualization version GIF version |
Description: The empty set is not a Moore collection. (Contributed by BJ, 9-Dec-2021.) |
Ref | Expression |
---|---|
bj-0nmoore | ⊢ ¬ ∅ ∈ Moore |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 4235 | . 2 ⊢ ¬ ∪ ∅ ∈ ∅ | |
2 | bj-ismoored0 34969 | . 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅) | |
3 | 1, 2 | mto 200 | 1 ⊢ ¬ ∅ ∈ Moore |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2110 ∅c0 4227 ∪ cuni 4809 Moorecmoore 34966 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2706 ax-sep 5181 ax-nul 5188 ax-pow 5247 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2713 df-cleq 2726 df-clel 2812 df-ral 3059 df-rab 3063 df-v 3403 df-dif 3860 df-in 3864 df-ss 3874 df-nul 4228 df-pw 4505 df-uni 4810 df-int 4850 df-bj-moore 34967 |
This theorem is referenced by: bj-snmooreb 34977 |
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