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Mirrors > Home > ILE Home > Th. List > df-card | 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. 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccrd 7116 | . 2 | |
2 | vx | . . 3 | |
3 | cvv 2712 | . . 3 | |
4 | vy | . . . . . . 7 | |
5 | 4 | cv 1334 | . . . . . 6 |
6 | 2 | cv 1334 | . . . . . 6 |
7 | cen 6685 | . . . . . 6 | |
8 | 5, 6, 7 | wbr 3967 | . . . . 5 |
9 | con0 4325 | . . . . 5 | |
10 | 8, 4, 9 | crab 2439 | . . . 4 |
11 | 10 | cint 3809 | . . 3 |
12 | 2, 3, 11 | cmpt 4027 | . 2 |
13 | 1, 12 | wceq 1335 | 1 |
Colors of variables: wff set class |
This definition is referenced by: cardcl 7118 isnumi 7119 cardval3ex 7122 |
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