Crossword Genius

Cleansing diet - I quit beef! (5)

Ross

I believe the answer is:

detox

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'cleansing' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'diet i quit beef' is the wordplay.
'quit' indicates named letters should be taken away.
'beef' becomes 'ox'.
'diet' with 'i' removed is 'det'.
'det'+'ox'='DETOX'

Can you help me to learn more?

(Other definitions for detox that I've seen before include "Purge" , "Remove poisons from the body" , "Rid of poison" , "What thalassotherapy may bring" , "possible treatment of alcoholic" .)

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