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 ) ) |