Description: Restricted coset of B . (Contributed by Peter Mazsa, 9-Dec-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | ecres | |- [ B ] ( R |` A ) = { x | ( B e. A /\ B R x ) } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elecres | |- ( x e. _V -> ( x e. [ B ] ( R |` A ) <-> ( B e. A /\ B R x ) ) ) |
|
2 | 1 | elv | |- ( x e. [ B ] ( R |` A ) <-> ( B e. A /\ B R x ) ) |
3 | 2 | abbi2i | |- [ B ] ( R |` A ) = { x | ( B e. A /\ B R x ) } |