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 ) |