Removing old Exchange server

Removing old Exchange server

We migrated an Exchange 2003 to exchange 2010 running on a new Windows
Server 2008 R2. The old Windows Server 2003 with Exchange 2003 is not
anymore (physically :-)) exist.
On my Exchange Server I saw event id 5006 MSEchangeTransport. When running
the Get-ExchangeServer cmdlet I still saw the old exchange server which
doesn't exist anymore.
I've followed these steps (http://support.microsoft.com/kb/833396) to go
to CN=Configuration, DC=Domain_Name,DC=com, CN=Services .... CN=Servers
Now I see on the CN=First Administrative Group > CN=Servers the old server
as only server listed and on the CN=Exchange Administrative Group >
CN=Servers I see the existing server as the only server listed.
Can I just remove that old server from the CN=Frist Administrative Group >
CN=Servers or should the new server also exist in the First Administrative
Group instead of only in the Exchange Administrative Group?
I'm using ADSI Edit on the Domain Controller, I suppose that there is no
difference on using it here or on the Exchange Server itself?