Woman and chap in middle American city (5)

I believe the answer is:

omaha

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'city' is the definition.
(Omaha is an example)

I cannot understand how the remainder of the clue works.

(Other definitions for omaha that I've seen before include "place in Nebraska" , "Nebraska city and code-named beach of D-Day landings" , "Where American may work" , "Cotton fabric used for curtains and upholstery" , "Largest city in Nebraska" .)

I've seen this clue in The Sun.

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