Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-card Unicode version

Definition df-card 8341
 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 8942 for its value, cardval2 8393 for a simpler version of its value. The principle theorem relating cardinality to equinumerosity is carden 8947. 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 8337 . 2
2 vx . . 3
3 cvv 3109 . . 3
4 vy . . . . . . 7
54cv 1394 . . . . . 6
62cv 1394 . . . . . 6
7 cen 7533 . . . . . 6
85, 6, 7wbr 4452 . . . . 5
9 con0 4883 . . . . 5
108, 4, 9crab 2811 . . . 4
1110cint 4286 . . 3
122, 3, 11cmpt 4510 . 2
131, 12wceq 1395 1
 Colors of variables: wff setvar class This definition is referenced by:  cardf2  8345  cardval3  8354
 Copyright terms: Public domain W3C validator