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That act lead to Claire living to meet her father, Nathan, and getting him to stop the bomb from happening, although presumably that would have happened in the future episode as well, so there's paradox #1.

In the Days of Future Past episode, Mr. Bennett says that she was in hiding and that people didn't know she was alive. It's possible that he put her in hiding immediately after she was "killed" in that timeline.
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Bitt Faulk