Multi-table UPDATE does not consider ORDER BY clause

CREATE TABLE AP (

 prid int not null,

 prio int not null

);

CREATE TABLE APD (

 prid int not null,

 info varchar(64)

);

INSERT INTO AP VALUES (1,3), (2,3), (3,2), (4,2), (5,1), (6,1);

INSERT INTO APD (prid) VALUES (1), (2), (3), (4), (5), (6);

SELECT * FROM AP;

SELECT * FROM APD;

# The SELECT returns the correct values for prid (prid 3,5,6) 

SELECT APD.prid, AP.prio FROM AP INNER JOIN APD ON AP.prid = APD.prid

 ORDER BY AP.prio, AP.prid

 LIMIT 3;

# The UPDATE with identical ORDER updates the columns with prid 1,2,3

UPDATE AP INNER JOIN APD ON AP.prid = APD.prid

 SET info = 'UPDATED'

 ORDER BY AP.prio, AP.prid

 LIMIT 3;

SELECT * FROM APD;

+------+------+

| prid | prio |

+------+------+

|    1 |    3 |

|    2 |    3 |

|    3 |    2 |

|    4 |    2 |

|    5 |    1 |

|    6 |    1 |

+------+------+

6 rows in set (0.001 sec)

+------+------+

| prid | info |

+------+------+

|    1 | NULL |

|    2 | NULL |

|    3 | NULL |

|    4 | NULL |

|    5 | NULL |

|    6 | NULL |

+------+------+

6 rows in set (0.000 sec)

+------+------+

| prid | prio |

+------+------+

|    5 |    1 |

|    6 |    1 |

|    3 |    2 |

+------+------+

3 rows in set (0.000 sec)

Query OK, 3 rows affected (0.001 sec)

Rows matched: 3  Changed: 3  Warnings: 0

+------+---------+

| prid | info    |

+------+---------+

|    1 | UPDATED |

|    2 | UPDATED |

|    3 | UPDATED |

|    4 | NULL    |

|    5 | NULL    |

|    6 | NULL    |

+------+---------+