Description: A restricted identity function is a continuous function. (Contributed by FL, 27-Dec-2006) (Proof shortened by Mario Carneiro, 21-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | idcn | |- ( J e. ( TopOn ` X ) -> ( _I |` X ) e. ( J Cn J ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid | |- J C_ J |
|
2 | ssidcn | |- ( ( J e. ( TopOn ` X ) /\ J e. ( TopOn ` X ) ) -> ( ( _I |` X ) e. ( J Cn J ) <-> J C_ J ) ) |
|
3 | 2 | anidms | |- ( J e. ( TopOn ` X ) -> ( ( _I |` X ) e. ( J Cn J ) <-> J C_ J ) ) |
4 | 1 3 | mpbiri | |- ( J e. ( TopOn ` X ) -> ( _I |` X ) e. ( J Cn J ) ) |