# A consequence of booleanity of the category of Set?

In Sheaves in Geometry and Logic one can find the following theorem:

Let $\mathcal{E}$ be an elementary topos which is generated by subobjects of $1$, and moreover has the property that for each object $E$, Sub$(E)$ is a complete Boolan algebra. Then $\mathcal{E}$ satisfies the axiom of choice (every epi splits).

Now, the category of Sets satisfies these two hypothesis but in general it does not verify the axiom of choice. What is wrong?!