Description: Membership in a power class. Theorem 86 of Suppes p. 47. (Contributed by NM, 11-Oct-2007)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | elpw2.1 | |- B e. _V |
|
| Assertion | elpw2 | |- ( A e. ~P B <-> A C_ B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elpw2.1 | |- B e. _V |
|
| 2 | elpw2g | |- ( B e. _V -> ( A e. ~P B <-> A C_ B ) ) |
|
| 3 | 1 2 | ax-mp | |- ( A e. ~P B <-> A C_ B ) |