Din in to the groom that's where he should eat (6,4)

I believe the answer is:

dining room

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'where he should eat' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'din in to the groom' is the wordplay.
'to the groom' becomes 'groom'.
'din'+'in'+'groom'='DINING-ROOM'

'that's' is the link.

Can you help me to learn more?

(Other definitions for dining room that I've seen before include "place for courses?" , "eating-place" , "mess" , "refectory" , "Where meals are eaten" .)

I've seen this clue in the Evening Standard.

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