Description: Membership in a quotient set. (Contributed by NM, 23-Jul-1995)
Ref | Expression | ||
---|---|---|---|
Assertion | elqsi | |- ( B e. ( A /. R ) -> E. x e. A B = [ x ] R ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elqsg | |- ( B e. ( A /. R ) -> ( B e. ( A /. R ) <-> E. x e. A B = [ x ] R ) ) |
|
2 | 1 | ibi | |- ( B e. ( A /. R ) -> E. x e. A B = [ x ] R ) |