For example, assume we are given a relation

**R**. For any particular x in

**dom R**, there exists some Y

0 for which xRY

0. And we can conclude that

for any x in dom R, there is a singleton {Y

0}included in {t| xRt}. We have not yet used the axiom of choice. what does require the axiom is

saying that for any x in

** dom R**, there is some Y

x for which xRY

x, and then putting all these Y

x's together into a set, e.g.,

{Y

x | x belongs to dom R}. This in effect is making many choices, one for each x in

**dom R**, which may be an infinite set.