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

I believe the answer is:

metropolis

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

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

'permit oslo or rome to slip badly' is the wordplay.
'permit oslo' anagrams to 'METROPOLIS'.
But, I'm unsure how the anagram is indicated.

'as' acts as a link.

Can you help me to learn more?

(Other definitions for metropolis that I've seen before include "chief centre" , "See" , "Expressionist movie" , "Main city" , "Big city" .)

I've seen this clue in The Telegraph.

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