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Is there any theorem or axiom on which substitution is based?

Or substituting is it a mere art?

Thanks in advance.

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    If you want a proof of chain rule (derivatives): http://en.wikipedia.org/wiki/Chain_rule, substitution rule (integrals): http://en.wikipedia.org/wiki/Substitution_rule. Substitution rule follows from chain rule.2011-12-03

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