Permit Oslo or Rome to slip badly as main city (10)

I believe the answer is:

metropolis

I'm a little stuck... Click here to teach me more about this clue!

'main city' is the definition.
(I've seen this before)

'permit oslo or rome to slip badly' is the wordplay.
'permit oslo' can be anagrammed to 'METROPOLIS'.
Though, I'm not sure how this is indicated.

'as' is the link.

Can you help me to learn more?

(Other definitions for metropolis that I've seen before include "Major city of region" , "Main city" , "Chief city" , "population centre" , "chief centre" .)

I've seen this clue in The Times.

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