Calling sp from in sql server db1 that inserts data to db2, with a login that has no access to db2

Question

I have 2 databases with named MainDB and MiddleDB , a limited user that has no access to MainDB but has full access to MiddleDB and also a power user with full access to MainDB and MiddleDB, and finally a stored procedure named sp_TransferData in MiddleDB for transfering Data from MiddleDB and insert them to MainDB' tables; When I call that sp, I got permission error. I try to use 'Execute As PowerUser' clause in sp definition, but I got same errors again.