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Mirrors > Home > MPE Home > Th. List > df-card | Structured version Visualization version Unicode version |
Description: Define the cardinal number function. The cardinal number of a set is the least ordinal number equinumerous to it. In other words, it is the "size" of the set. Definition of [Enderton] p. 197. See cardval 8997 for its value, cardval2 8451 for a simpler version of its value. The principle theorem relating cardinality to equinumerosity is carden 9002. Our notation is from Enderton. Other textbooks often use a double bar over the set to express this function. (Contributed by NM, 21-Oct-2003.) |
Ref | Expression |
---|---|
df-card |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccrd 8395 |
. 2
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2 | vx |
. . 3
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3 | cvv 3057 |
. . 3
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4 | vy |
. . . . . . 7
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5 | 4 | cv 1454 |
. . . . . 6
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6 | 2 | cv 1454 |
. . . . . 6
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7 | cen 7592 |
. . . . . 6
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8 | 5, 6, 7 | wbr 4416 |
. . . . 5
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9 | con0 5442 |
. . . . 5
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10 | 8, 4, 9 | crab 2753 |
. . . 4
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11 | 10 | cint 4248 |
. . 3
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12 | 2, 3, 11 | cmpt 4475 |
. 2
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13 | 1, 12 | wceq 1455 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: cardf2 8403 cardval3 8412 |
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