+--------+-------+------+--+
| Object | Event | Time |  |
+--------+-------+------+--+
| Obj1   | A     |    1 |  |
| Obj1   | B     |    3 |  |
| Obj2   | A     |    7 |  |
| Obj2   | B     |    4 |  |
+--------+-------+------+--+

SELECT DISTINCT Object from
(SELECT * from
(SELECT * FROM table
INNER JOIN (SELECT Object Obj FROM table WHERE event LIKE '%A%' AS temp_table
ON table.Object=temp_table.Obj) AS temp_final WHERE event LIKE '%B%')
AS temp2;

Obj1