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Yes, but it doesn't make sense to ask "Is a=a?" And if x=y, then asking "Is x=y?" is the same thing as asking "Is x=x?" The reason you can add it into a proof at any time is because it doesn't mean anything -- it doesn't add any new information into the proof, and is precisely for this reason admissible. Would you ever ask "Is 2=2?" or "Is Aristotle Aristotle?"
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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