Description: Membership in an ordered-pair class abstraction defined by a restricted binary relation. (Contributed by AV, 16-Feb-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | elopabran | |- ( A e. { <. x , y >. | ( x R y /\ ps ) } -> A e. R ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl | |- ( ( x R y /\ ps ) -> x R y ) |
|
2 | 1 | ssopab2i | |- { <. x , y >. | ( x R y /\ ps ) } C_ { <. x , y >. | x R y } |
3 | opabss | |- { <. x , y >. | x R y } C_ R |
|
4 | 2 3 | sstri | |- { <. x , y >. | ( x R y /\ ps ) } C_ R |
5 | 4 | sseli | |- ( A e. { <. x , y >. | ( x R y /\ ps ) } -> A e. R ) |