Description: If a set is finite, its converse is as well. (Contributed by Mario Carneiro, 28-Dec-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | cnvfi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvcnvss | ||
2 | ssfi | ||
3 | 1 2 | mpan2 | |
4 | relcnv | ||
5 | cnvexg | ||
6 | cnven | ||
7 | 4 5 6 | sylancr | |
8 | enfii | ||
9 | 3 7 8 | syl2anc |