I want to update record of a table through another database with equal columns

Question

I want to update the ordem_subclass column of the Prod_serv Table, and the reference are the codecolumns of the Prod_serv Table and code of the Subclass Table:

USE S9_Real
UPDATE Prod_Serv SET
Ordem_Subclasse = SC.ORDEM
FROM Prod_Serv PS
INNER JOIN S9_Real_MP2.DBO.Prod_Serv MP2PS ON PS.Codigo = MP2PS.Codigo
INNER JOIN S9_REAL_MP2.DBO.Subclasses MP2SC ON PS.Codigo = MP2PS.Codigo
INNER JOIN Subclasses SC ON SC.Codigo = MP2SC.Codigo
WHERE SC.Codigo = MP2SC.Codigo