My bad I was giving you a high level example that you did not understand with the other country example. Replace the other country just for thought with your city example...
The PCC since it has to be current dated has to be in your previous address
You will anyhow indicate as part of the PR application where all have you stayed in the last 10 yrs that will provide the case officer all the details what was your old address and what is the new address
No you dont need to mention anything just submit with the document you have mention in the PR application the present address that you are residing on. No changes no affidavit no loe nothing is required