Description: Obsolete theorem, use hffi instead. Hereditarily finite sets are finite sets. (Contributed by BTernaryTau, 30-Dec-2025) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | r1omfi | |- U. ( R1 " _om ) C_ Fin |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-hf | |- HF = U. ( R1 " _om ) |
|
| 2 | 1 | eleq2i | |- ( x e. HF <-> x e. U. ( R1 " _om ) ) |
| 3 | hffi | |- ( x e. HF -> x e. Fin ) |
|
| 4 | 2 3 | sylbir | |- ( x e. U. ( R1 " _om ) -> x e. Fin ) |
| 5 | 4 | ssriv | |- U. ( R1 " _om ) C_ Fin |