Description: Any set is equinumerous to its cardinal number. Proposition 10.5 of TakeutiZaring p. 85. (Contributed by NM, 22-Oct-2003) (Revised by Mario Carneiro, 28-Apr-2015)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | cardval.1 | |- A e. _V |
|
| Assertion | cardid | |- ( card ` A ) ~~ A |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cardval.1 | |- A e. _V |
|
| 2 | numth3 | |- ( A e. _V -> A e. dom card ) |
|
| 3 | cardid2 | |- ( A e. dom card -> ( card ` A ) ~~ A ) |
|
| 4 | 1 2 3 | mp2b | |- ( card ` A ) ~~ A |