Description: A singleton of a set belongs to the power class of a class containing the set. (Contributed by NM, 1-Apr-1998)
Ref | Expression | ||
---|---|---|---|
Hypothesis | snelpw.1 | |- A e. _V |
|
Assertion | snelpw | |- ( A e. B <-> { A } e. ~P B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snelpw.1 | |- A e. _V |
|
2 | 1 | snss | |- ( A e. B <-> { A } C_ B ) |
3 | snex | |- { A } e. _V |
|
4 | 3 | elpw | |- ( { A } e. ~P B <-> { A } C_ B ) |
5 | 2 4 | bitr4i | |- ( A e. B <-> { A } e. ~P B ) |