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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 4326 | . 2 ⊢ ¬ ∪ ∅ ∈ ∅ | |
2 | bj-ismoored0 36575 | . 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅) | |
3 | 1, 2 | mto 196 | 1 ⊢ ¬ ∅ ∈ Moore |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2099 ∅c0 4318 ∪ cuni 4903 Moorecmoore 36572 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2698 ax-sep 5293 ax-nul 5300 ax-pow 5359 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-ral 3057 df-rex 3066 df-rab 3428 df-v 3471 df-dif 3947 df-in 3951 df-ss 3961 df-nul 4319 df-pw 4600 df-uni 4904 df-int 4945 df-bj-moore 36573 |
This theorem is referenced by: bj-snmooreb 36583 |
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