Description: Alternate definition of quotient set. (Contributed by Steven Nguyen, 7-Jun-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | dfqs2 | |- ( A /. R ) = ran ( x e. A |-> [ x ] R ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-qs | |- ( A /. R ) = { y | E. x e. A y = [ x ] R } |
|
2 | eqid | |- ( x e. A |-> [ x ] R ) = ( x e. A |-> [ x ] R ) |
|
3 | 2 | rnmpt | |- ran ( x e. A |-> [ x ] R ) = { y | E. x e. A y = [ x ] R } |
4 | 1 3 | eqtr4i | |- ( A /. R ) = ran ( x e. A |-> [ x ] R ) |