Let $\displaystyle \phi (v)$ be a formula of the languages of set theory. Let X be a set. Then the following is a set:$\displaystyle \{a \in X|\phi [a] \} $, ie all the elements of X with the property $\displaystyle \phi$ form a set.

Write down a formula $\displaystyle \phi (v)$ saying that "v is a set which has exactly three elements".

I would like to check whether it is possible to represent the above statement as this: $\displaystyle \exists x_1 \exists x_2 \exists x_3 ((x_1 \in v \wedge x_2 \in v \wedge x_3 \in v) \wedge \forall y (y \in v \longrightarrow (y = x_1 \vee y = x_2 \vee y = x_3 ))$

Thanks in advance.