Description: The range of a finite set is finite. (Contributed by Mario Carneiro, 28-Dec-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | rnfi | |- ( A e. Fin -> ran A e. Fin ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn | |- ran A = dom `' A |
|
2 | cnvfi | |- ( A e. Fin -> `' A e. Fin ) |
|
3 | dmfi | |- ( `' A e. Fin -> dom `' A e. Fin ) |
|
4 | 2 3 | syl | |- ( A e. Fin -> dom `' A e. Fin ) |
5 | 1 4 | eqeltrid | |- ( A e. Fin -> ran A e. Fin ) |