Description: A relation (set) is finite if and only if both its domain and range are finite. (Contributed by Thierry Arnoux, 27-Aug-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | relfi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmfi | |
|
2 | rnfi | |
|
3 | 1 2 | jca | |
4 | xpfi | |
|
5 | relssdmrn | |
|
6 | ssfi | |
|
7 | 4 5 6 | syl2anr | |
8 | 7 | ex | |
9 | 3 8 | impbid2 | |