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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-lines | Structured version Visualization version Unicode version |
Description: Define set of all projective lines for a Hilbert lattice (actually in any set at all, for simplicity). The join of two distinct atoms equals a line. Definition of lines in item 1 of [Holland95] p. 222. (Contributed by NM, 19-Sep-2011.) |
Ref | Expression |
---|---|
df-lines |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clines 33061 |
. 2
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2 | vk |
. . 3
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3 | cvv 3013 |
. . 3
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4 | vq |
. . . . . . . . 9
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5 | 4 | cv 1447 |
. . . . . . . 8
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6 | vr |
. . . . . . . . 9
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7 | 6 | cv 1447 |
. . . . . . . 8
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8 | 5, 7 | wne 2622 |
. . . . . . 7
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9 | vs |
. . . . . . . . 9
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10 | 9 | cv 1447 |
. . . . . . . 8
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11 | vp |
. . . . . . . . . . 11
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12 | 11 | cv 1447 |
. . . . . . . . . 10
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13 | 2 | cv 1447 |
. . . . . . . . . . . 12
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14 | cjn 16200 |
. . . . . . . . . . . 12
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15 | 13, 14 | cfv 5561 |
. . . . . . . . . . 11
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16 | 5, 7, 15 | co 6276 |
. . . . . . . . . 10
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17 | cple 15208 |
. . . . . . . . . . 11
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18 | 13, 17 | cfv 5561 |
. . . . . . . . . 10
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19 | 12, 16, 18 | wbr 4374 |
. . . . . . . . 9
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20 | catm 32831 |
. . . . . . . . . 10
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21 | 13, 20 | cfv 5561 |
. . . . . . . . 9
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22 | 19, 11, 21 | crab 2741 |
. . . . . . . 8
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23 | 10, 22 | wceq 1448 |
. . . . . . 7
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24 | 8, 23 | wa 375 |
. . . . . 6
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25 | 24, 6, 21 | wrex 2738 |
. . . . 5
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26 | 25, 4, 21 | wrex 2738 |
. . . 4
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27 | 26, 9 | cab 2438 |
. . 3
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28 | 2, 3, 27 | cmpt 4433 |
. 2
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29 | 1, 28 | wceq 1448 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: lineset 33305 |
Copyright terms: Public domain | W3C validator |