How to remove my Photo Stream from my phone without losing any photos I need to make space on my phone to upgrade iOS, and an 800 MB Photo Stream looks like a pretty good candidate for removal.  The only problem is that it's very unclear to me what happens if I remove the Photo Stream: are the photos deleted from other devices?  (I'm not talking about deleting individual photos from the photo stream, but rather turning off Photo Stream on that device.  Apple doesn't make the consequences of that action 100% clear, and things I've read (which I hope are wrong) suggest that any removal on one device is carried over to other devices.
What happens to my photos if I turn off My Photo Stream?
If you sign out of iCloud or turn off My Photo Stream on an iOS device, all the images in My Photo Stream are removed from that device. The images in My Photo Stream on your other devices are not affected. Images added to My Photo Stream are saved on the iCloud server for 30 days from the date you added them to My Photo Stream. If you sign in to iCloud with the same Apple ID and turn on My Photo Stream on another device, those photos will automatically download to this device. Before turning off My Photo Stream, it's a good idea to save any photos that you'd like to keep to your Camera Roll. Learn more about saving your photos to your Camera Roll.

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