Description: A pair of two sets belongs to the power class of a class containing those two sets. (Contributed by Thierry Arnoux, 10-Mar-2017) (Proof shortened by AV, 23-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | prelpwi | |- ( ( A e. C /\ B e. C ) -> { A , B } e. ~P C ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | prelpw | |- ( ( A e. C /\ B e. C ) -> ( ( A e. C /\ B e. C ) <-> { A , B } e. ~P C ) ) |
|
| 2 | 1 | ibi | |- ( ( A e. C /\ B e. C ) -> { A , B } e. ~P C ) |