Description: A class cannot be an element of one of its elements. (Contributed by AV, 14-Jun-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | elnel | |- ( A e. B -> B e/ A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elnotel | |- ( A e. B -> -. B e. A ) |
|
2 | df-nel | |- ( B e/ A <-> -. B e. A ) |
|
3 | 1 2 | sylibr | |- ( A e. B -> B e/ A ) |