Description: There is exactly one element in a singleton. Exercise 2 of TakeutiZaring p. 15. This variation requires only that B , rather than A , be a set. (Contributed by NM, 12-Jun-1994)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | elsn2.1 | |- B e. _V |
|
| Assertion | elsn2 | |- ( A e. { B } <-> A = B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elsn2.1 | |- B e. _V |
|
| 2 | elsn2g | |- ( B e. _V -> ( A e. { B } <-> A = B ) ) |
|
| 3 | 1 2 | ax-mp | |- ( A e. { B } <-> A = B ) |