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Section 2.2: Problem 4 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R. Munkres
Show that if does not occur free in , then .
For every structure and such that , we note that, for all , and agree at all free variables in , then, according to Theorem 22A, for all , , i.e. .