Description: All elements of a class are elements of a class equal to this class. (Contributed by AV, 30-Oct-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | raleleq | |- ( A = B -> A. x e. A x e. B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralel | |- A. x e. B x e. B |
|
2 | id | |- ( A = B -> A = B ) |
|
3 | 2 | raleqdv | |- ( A = B -> ( A. x e. A x e. B <-> A. x e. B x e. B ) ) |
4 | 1 3 | mpbiri | |- ( A = B -> A. x e. A x e. B ) |