Gets rid of a book he soils badly (9)

I believe the answer is:

abolishes

'gets rid of' is the definition.
('abolish' can be a synonym of 'get rid of')

'a book he soils badly' is the wordplay.
'book' becomes 'b' (abbreviation for book).
'badly' indicates an anagram (letters in the wrong order).
'he'+'soils'='hesoils'
'hesoils' is an anagram of 'olishes'.
'a'+'b'+'olishes'='ABOLISHES'

I've seen this clue in The Times.

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