Description: Let us define a cardinal number to be an element A e. On such that A is not equipotent with any x e. A . (Contributed by RP, 1-Oct-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | elrncard | |- ( A e. ran card <-> ( A e. On /\ A. x e. A -. x ~~ A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iscard4 | |- ( ( card ` A ) = A <-> A e. ran card ) |
|
2 | iscard5 | |- ( ( card ` A ) = A <-> ( A e. On /\ A. x e. A -. x ~~ A ) ) |
|
3 | 1 2 | bitr3i | |- ( A e. ran card <-> ( A e. On /\ A. x e. A -. x ~~ A ) ) |