SQL Query with "feedback loop"

Currently, I am using MySQL

I have 2 tables:

Table objects:

| id | desc |
| 1  | 'A'  |
| 2  | 'B'  |
| 3  | 'C'  |
| 4  | 'D'  |
| 5  | 'E'  |

Table implies:

| id1 | id2 |
| 1   | 2   |
| 1   | 3   |
| 2   | 4   |
| 2   | 5   |
| 3   | 5   |

Table Implies columns id1 and id2 are both foreign keys to table objects id.

Which means:

object 1 implies object 2 and object 3.

object 2 implies object 4 and object 5

object 3 implies object 5

Therefore, Object 1, implies 2, 3, and 4 and 5 (Since 2 implies 4 and 5)

Is there any way to create a query for this behaviour? My current solution consists on calling recursively from java the query until I don't get any new info:

SQL Query Im calling:

SELECT o.id, i.id2 
FROM objects o 
    INNER JOIN implies i ON o.id = i.id1 WHERE id = 1;

I first call it with id = 1, then with id IN (2, 3)... etc

The kind of result I want to achieve:

SELECT ... WHERE id = 1

should return:

| id | id2  |
| 1  | 2    |
| 1  | 3    |
| 1  | 4    |
| 1  | 5    |