Description: Membership in a power class. Theorem 86 of Suppes p. 47. (Contributed by NM, 31-Dec-1993) (Proof shortened by BJ, 31-Dec-2023)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | elpw.1 | |- A e. _V |
|
| Assertion | elpw | |- ( A e. ~P B <-> A C_ B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elpw.1 | |- A e. _V |
|
| 2 | elpwg | |- ( A e. _V -> ( A e. ~P B <-> A C_ B ) ) |
|
| 3 | 1 2 | ax-mp | |- ( A e. ~P B <-> A C_ B ) |