Description: The value of the birthday function is always an ordinal. (Contributed by Scott Fenton, 14-Jun-2011) (Proof shortened by Scott Fenton, 8-Dec-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | bdayelon | |- ( bday ` A ) e. On |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bdayfo | |- bday : No -onto-> On |
|
| 2 | fof | |- ( bday : No -onto-> On -> bday : No --> On ) |
|
| 3 | 1 2 | ax-mp | |- bday : No --> On |
| 4 | 0elon | |- (/) e. On |
|
| 5 | 3 4 | f0cli | |- ( bday ` A ) e. On |