Is SQLite index automatically removed when its table is dropped?

Say, if I first did the following to create a table using SQLite3 databse:

CREATE TABLE `t3` (
    `f0` INTEGER PRIMARY KEY AUTOINCREMENT, 
    `f1` INTEGER NOT NULL REFERENCES `t2`(`f0`) ON DELETE CASCADE, 
    `f2` INTEGER NOT NULL REFERENCES `t1`(`f0`) ON DELETE CASCADE, 
    `f3` INTEGER NOT NULL, 
    `f4` BLOB, 
    `f5` BLOB, 
    `f6` BLOB, 
    `f7` BLOB, 
    `f8` BLOB, 
    `f9` BLOB, 
    `fa` BLOB)

and then created an index on that table:

CREATE INDEX `it31` ON `t3`(`f1`)

So after this table had some rows inserted into it, if I removed it by doing:

DROP TABLE `t3`

Does it also remove the it31 index, or do I need to remove the index prior to removing the table?