Crossword Genius

Single act in spoof put out by the same act (4,5)

Ross

I believe the answer is:

ipso facto

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'by the same act' is the definition.
I can't tell whether this definition defines the answer.

'single act in spoof put out' is the wordplay.
'single' becomes 'I' (one).
'in' is an insertion indicator.
'put out' indicates an anagram.
'spoof' with letters rearranged gives 'psofo'.
'act' going within 'psofo' is 'psofacto'.
'i'+'psofacto'='IPSO-FACTO'

Can you help me to learn more?

(Other definitions for ipso facto that I've seen before include "By that very fact" , "by the very nature of the case)" , "Self-evidently; thereby" , "By that very act (Lat.)" , "For that precise reason" .)

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