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.
.