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Phrase(s): drink something up
to drink all of something that is served or that is on hand. • Who drank all the root beer up? • I drank up the root beer., Phrase(s): Drink up!
Finish your drink!; Finish that drink, and we’ll have another! • Okay, drink up! It’s closing time. • Drink up, and let’s get going.
McGrawhill's American Idioms And Phrasal Verbs