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Is there any quick way to delete all songs from library without them being removed from playlists?
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If they're not in the library then they cannot be in the playlists. Do you perhaps have a subscription to Apple Music or iTunes Match? With one of these services you can use the remove download option for locally stored music to free up storage space and stream the tracks from the cloud. You should take a complete backup of your library on an external drive before your proceed in case you are unhappy with any of the matches, or you delete something in error.
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