Description: A set is the union of its finite subsets. (Contributed by Stefan O'Rear, 2-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | unifpw | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inss1 | |
|
2 | 1 | unissi | |
3 | unipw | |
|
4 | 2 3 | sseqtri | |
5 | 4 | sseli | |
6 | snelpwi | |
|
7 | snfi | |
|
8 | 7 | a1i | |
9 | 6 8 | elind | |
10 | elssuni | |
|
11 | 9 10 | syl | |
12 | snidg | |
|
13 | 11 12 | sseldd | |
14 | 5 13 | impbii | |
15 | 14 | eqriv | |