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Mirrors > Home > NFE Home > Th. List > df-xpk | Unicode version |
Description: Define the Kuratowski cross product. This definition through df-idk 4196 set up the Kuratowski relationships. These are used mainly to prove the properties of df-op 4567, and are not used thereafter. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
df-xpk |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . 3
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2 | cB |
. . 3
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3 | 1, 2 | cxpk 4175 |
. 2
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4 | vx |
. . . . . . . 8
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5 | 4 | cv 1641 |
. . . . . . 7
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6 | vy |
. . . . . . . . 9
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7 | 6 | cv 1641 |
. . . . . . . 8
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8 | vz |
. . . . . . . . 9
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9 | 8 | cv 1641 |
. . . . . . . 8
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10 | 7, 9 | copk 4058 |
. . . . . . 7
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11 | 5, 10 | wceq 1642 |
. . . . . 6
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12 | 7, 1 | wcel 1710 |
. . . . . . 7
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13 | 9, 2 | wcel 1710 |
. . . . . . 7
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14 | 12, 13 | wa 358 |
. . . . . 6
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15 | 11, 14 | wa 358 |
. . . . 5
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16 | 15, 8 | wex 1541 |
. . . 4
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17 | 16, 6 | wex 1541 |
. . 3
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18 | 17, 4 | cab 2339 |
. 2
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19 | 3, 18 | wceq 1642 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: elxpk 4197 xpkssvvk 4211 opkelxpkg 4248 |
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