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Definition df-card 7456
 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 8052 for its value, cardval2 7508 for a simpler version of its value. The principle theorem relating cardinality to equinumerosity is carden 8055. 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.)
Assertion
Ref Expression
df-card
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-card
StepHypRef Expression
1 ccrd 7452 . 2
2 vx . . 3
3 cvv 2727 . . 3
4 vy . . . . . . 7
54cv 1618 . . . . . 6
62cv 1618 . . . . . 6
7 cen 6746 . . . . . 6
85, 6, 7wbr 3920 . . . . 5
9 con0 4285 . . . . 5
108, 4, 9crab 2512 . . . 4
1110cint 3760 . . 3
122, 3, 11cmpt 3974 . 2
131, 12wceq 1619 1
 Colors of variables: wff set class This definition is referenced by:  cardf2  7460  cardval3  7469
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