I had a house in American state (5)

I believe the answer is:

idaho

'american state' is the definition.
(Idaho is an example)

'i had a house' is the wordplay.
'i had' becomes 'id' (I'd).
'house' becomes 'ho' (abbreviation for house).
'id'+'a'+'ho'='IDAHO'

'in' acts as a link.

(Other definitions for idaho that I've seen before include "North-western US state" , "State of northwest US" , "US state in the Rocky Mountains" , "One of 22 Across, capital Boise" , "North-western state of America" .)

I've seen this clue in The Times.

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