Definition of back down phrasal verb from the Oxford Advanced Learner's Dictionary

 

back down

 phrasal verb
phrasal verb
 
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Phrasal Verbs

back down

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back down from something

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back down on something

(North American English also back off)
 
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to take back a demand, an opinion, etc. that other people are strongly opposed to; to admit defeat She refused to back down on a point of principle.
See the Oxford Advanced American Dictionary entry: back down