Description: Define negated membership. (Contributed by NM, 7-Aug-1994)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-nel | |- ( A e/ B <-> -. A e. B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | cA | |- A |
|
| 1 | cB | |- B |
|
| 2 | 0 1 | wnel | |- A e/ B |
| 3 | 0 1 | wcel | |- A e. B |
| 4 | 3 | wn | |- -. A e. B |
| 5 | 2 4 | wb | |- ( A e/ B <-> -. A e. B ) |