Making hard boiled eggs. Lets say you start boiling the eggs to make hard boiled eggs, but something came up that you had to attend to, so?

you stopped boiling the eggs, let them cool and stuck the-not-completely-cooked eggs into the refrigerator. You came back hours later. Could you then re-cook the eggs to the hard boiled stage? Would the hard boiled texture come out just fine, the 2nd time? Why or Why Not?
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