Description: The restricted identity relation expressed in maps-to notation. (Contributed by FL, 25-Apr-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | mptresid | |- ( _I |` A ) = ( x e. A |-> x ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opabresid | |- ( _I |` A ) = { <. x , y >. | ( x e. A /\ y = x ) } |
|
2 | df-mpt | |- ( x e. A |-> x ) = { <. x , y >. | ( x e. A /\ y = x ) } |
|
3 | 1 2 | eqtr4i | |- ( _I |` A ) = ( x e. A |-> x ) |