Description: The collection of finite subsets of a set dominates the set. (We use the weaker sethood assumption ( ~P A i^i Fin ) e. _V because this theorem also implies that A is a set if ~P A i^i Fin is.) (Contributed by Mario Carneiro, 17-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | infpwfidom | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snelpwi | |
|
2 | snfi | |
|
3 | 2 | a1i | |
4 | 1 3 | elind | |
5 | sneqbg | |
|
6 | 5 | adantr | |
7 | 4 6 | dom2 | |