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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 4062 | . 2 ⊢ ¬ ∪ ∅ ∈ ∅ | |
2 | bj-ismoored0 33367 | . 2 ⊢ (∅ ∈ Moore → ∪ ∅ ∈ ∅) | |
3 | 1, 2 | mto 188 | 1 ⊢ ¬ ∅ ∈ Moore |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∈ wcel 2139 ∅c0 4058 ∪ cuni 4588 Moorecmoore 33363 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-9 2148 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 ax-ext 2740 ax-nul 4941 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1635 df-ex 1854 df-nf 1859 df-sb 2047 df-clab 2747 df-cleq 2753 df-clel 2756 df-nfc 2891 df-ral 3055 df-rex 3056 df-v 3342 df-dif 3718 df-in 3722 df-ss 3729 df-nul 4059 df-pw 4304 df-uni 4589 df-int 4628 df-bj-moore 33364 |
This theorem is referenced by: bj-snmoore 33374 |
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