Can I use ellipses in first order logic

Question

I ask, because I have to come up with a first-order logic sentence that shows that there are exactly N objects in the universe. What I've been able to come up with is:

$$ \forall x \; \exists y_1, y_2, \dots , y_{n-1} \; (x \neq y_1) \land (x \neq y_2) \land \dots \land (x \neq y_{n-1})$$

I'm not sure if this is a valid first-order logic sentence or not.