Description: A class is a set iff it is a member of its singleton. (Contributed by NM, 5-Apr-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | snidb | |- ( A e. _V <-> A e. { A } ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg | |- ( A e. _V -> A e. { A } ) |
|
2 | elex | |- ( A e. { A } -> A e. _V ) |
|
3 | 1 2 | impbii | |- ( A e. _V <-> A e. { A } ) |