No. You can not use My Photo Stream to backup your photos instead of iCloud backup or iTunes. Photos in My Photo Stream are saved on the iCloud server for 30 days. To backup these photos, you must save them to your iOS device from My Photo Stream. To save photos to iOS device from My Photo Stream, select the photos and tap "Share" button and then tap "Save Image" button. Once you have saved your photos to iOS device, you can backup photos using iCloud or iTunes. If you enabled iCloud Photo Library, your photos and videos are automatically uploaded to iCloud at full resolution.
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