Speak vehemently in former demand (7)

I believe the answer is:

exclaim

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'speak vehemently' is the definition.
'exclaim' can be an answer for 'speak' (thesaurus). I'm not certain of the 'vehemently' bit.

'former demand' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'demand' becomes 'claim' (claiming is a kind of demanding).
'ex'+'claim'='EXCLAIM'

'in' is the link.

Can you help me to learn more?

(Other definitions for exclaim that I've seen before include "speak out boldly" , "Express surprise" , "Speak suddenly" , "Utter boldly" , "Declare" .)

I've seen this clue in the Sydney Morning Herald.

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