Description: The domain of a finite set is finite. (Contributed by Mario Carneiro, 24-Sep-2013)
Ref | Expression | ||
---|---|---|---|
Assertion | dmfi | |- ( A e. Fin -> dom A e. Fin ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fidomdm | |- ( A e. Fin -> dom A ~<_ A ) |
|
2 | domfi | |- ( ( A e. Fin /\ dom A ~<_ A ) -> dom A e. Fin ) |
|
3 | 1 2 | mpdan | |- ( A e. Fin -> dom A e. Fin ) |