Uncover the truth to nude dancing: a form of English vice (9)

I believe the answer is:

undeceive

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'uncover the truth' is the definition.
I can't tell whether this defines the answer.

'nude dancing a form of english vice' is the wordplay.
'dancing' is an anagram indicator.
'a form of' indicates an anagram (another form of the same letters).
'english' becomes 'E' (abbreviation).
'nude' with letters rearranged gives 'unde'.
'e'+'vice'='evice'
'evice' is an anagram of 'ceive'.
'unde'+'ceive'='UNDECEIVE'

'to' acts as a link.

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