axiomatic sets 37 (axiom of choice)

For any non-empty set $\mathcal{A}$ , there is a function $f$
which can pick up an element $a$ from every each set $A$ in $\mathcal{A}$.
The collection of all $a$ is a set, and $f$ is called a choice function.


Do you think it is obvious or a self-evident truth?