Description: Any ordinal number is equinumerous to its cardinal number. Unlike cardid , this theorem does not require the Axiom of Choice. (Contributed by NM, 26-Jul-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | oncardid | |- ( A e. On -> ( card ` A ) ~~ A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | onenon | |- ( A e. On -> A e. dom card ) |
|
2 | cardid2 | |- ( A e. dom card -> ( card ` A ) ~~ A ) |
|
3 | 1 2 | syl | |- ( A e. On -> ( card ` A ) ~~ A ) |