Step |
Hyp |
Ref |
Expression |
1 |
|
brcnvg |
|- ( ( x e. _V /\ u e. _V ) -> ( x `' R u <-> u R x ) ) |
2 |
1
|
el2v |
|- ( x `' R u <-> u R x ) |
3 |
2
|
anbi1i |
|- ( ( x `' R u /\ u R y ) <-> ( u R x /\ u R y ) ) |
4 |
3
|
exbii |
|- ( E. u ( x `' R u /\ u R y ) <-> E. u ( u R x /\ u R y ) ) |
5 |
4
|
opabbii |
|- { <. x , y >. | E. u ( x `' R u /\ u R y ) } = { <. x , y >. | E. u ( u R x /\ u R y ) } |
6 |
|
df-co |
|- ( R o. `' R ) = { <. x , y >. | E. u ( x `' R u /\ u R y ) } |
7 |
|
df-coss |
|- ,~ R = { <. x , y >. | E. u ( u R x /\ u R y ) } |
8 |
5 6 7
|
3eqtr4ri |
|- ,~ R = ( R o. `' R ) |