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Mirrors > Home > MPE Home > Th. List > df-clat | Structured version Visualization version Unicode version |
Description: Define the class of all complete lattices, where every subset of the base set has an LUB and a GLB. (Contributed by NM, 18-Oct-2012.) (Revised by NM, 12-Sep-2018.) |
Ref | Expression |
---|---|
df-clat |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccla 16401 |
. 2
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2 | vp |
. . . . . . . 8
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3 | 2 | cv 1453 |
. . . . . . 7
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4 | club 16235 |
. . . . . . 7
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5 | 3, 4 | cfv 5600 |
. . . . . 6
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6 | 5 | cdm 4852 |
. . . . 5
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7 | cbs 15169 |
. . . . . . 7
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8 | 3, 7 | cfv 5600 |
. . . . . 6
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9 | 8 | cpw 3962 |
. . . . 5
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10 | 6, 9 | wceq 1454 |
. . . 4
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11 | cglb 16236 |
. . . . . . 7
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12 | 3, 11 | cfv 5600 |
. . . . . 6
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13 | 12 | cdm 4852 |
. . . . 5
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14 | 13, 9 | wceq 1454 |
. . . 4
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15 | 10, 14 | wa 375 |
. . 3
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16 | cpo 16233 |
. . 3
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17 | 15, 2, 16 | crab 2752 |
. 2
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18 | 1, 17 | wceq 1454 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: isclat 16403 |
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