Description: Membership in an ordered-pair class abstraction defined by a binary relation. (Contributed by AV, 16-Feb-2021) (Proof shortened by SN, 11-Dec-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | elopabr | |- ( A e. { <. x , y >. | x R y } -> A e. R ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | opabss | |- { <. x , y >. | x R y } C_ R |
|
| 2 | 1 | sseli | |- ( A e. { <. x , y >. | x R y } -> A e. R ) |