EDIT: People are the bigger disccusion thread (https://news.ycombinator.com/item?id=6502756) are saying that it's possible to update without deleting/restore by downloading the ipsw and alt+click the "check for updates button".
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Original:
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Booting to recovery mode (http://support.apple.com/kb/HT1808) and clicking restore will download the 7.0.2 firmware (no need to alt+restore), wipe the phone, and update to 7.0.2
I was getting offered 6.1.3 and not 7.0.2 because my itunes wasn't updated to 11.1+.
Before booting to recovery mode, copy over your camera roll with image capture/aperture/iphoto just in case your latest backup (iCloud or iTunes) isn't up to date.
--- Original: --- Booting to recovery mode (http://support.apple.com/kb/HT1808) and clicking restore will download the 7.0.2 firmware (no need to alt+restore), wipe the phone, and update to 7.0.2
I was getting offered 6.1.3 and not 7.0.2 because my itunes wasn't updated to 11.1+.
Before booting to recovery mode, copy over your camera roll with image capture/aperture/iphoto just in case your latest backup (iCloud or iTunes) isn't up to date.