Description: A finite set is equinumerous to its cardinal number. (Contributed by Mario Carneiro, 21-Sep-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | ficardid | |- ( A e. Fin -> ( card ` A ) ~~ A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | finnum | |- ( A e. Fin -> A e. dom card ) |
|
2 | cardid2 | |- ( A e. dom card -> ( card ` A ) ~~ A ) |
|
3 | 1 2 | syl | |- ( A e. Fin -> ( card ` A ) ~~ A ) |