Definition of finish with phrasal verb from the Oxford Advanced American Dictionary

 

finish with

 phrasal verb
phrasal verb
 
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Phrasal Verbs

    finish with something

     
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  1. 1 to no longer need to use something When you're finished with the book, can I see it?
  2. 2 (informal) to stop doing something I'm finished with gambling.

finish (up) with something

 
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to have something at the end We had a five-course lunch and finished up with coffee and mints. We'll finish with a few songs.
See the Oxford Advanced Learner's Dictionary entry: finish with