Deleting all rows from INNER JOINed 3 different tables
If you have more than one join you could use comma separated USING statements:

DELETE 
FROM 
      AAA AS a 
USING 
      BBB AS b,
      CCC AS c
WHERE 
      a.id = b.id 
  AND a.id = c.id
  AND a.uid = 12345 
  AND c.gid = 's434sd4'


Reference