Description: A restricted class built from a finite set is finite. (Contributed by Thierry Arnoux, 14-Feb-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | rabfi | |- ( A e. Fin -> { x e. A | ph } e. Fin ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfrab3 | |- { x e. A | ph } = ( A i^i { x | ph } ) |
|
2 | infi | |- ( A e. Fin -> ( A i^i { x | ph } ) e. Fin ) |
|
3 | 1 2 | eqeltrid | |- ( A e. Fin -> { x e. A | ph } e. Fin ) |