hinge on

hinge on idiom
Also, hinge upon. Depend or be contingent on, as in This plan hinges on her approval. This expression employs the verb hinge in the sense of “to hang,” as a door would hang on a hinge, a usage dating from the early 1700s.

The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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