Set builder notation with $\land$?

Question

Is it possible to rewrite set builder notation with conjunction $\land$?

For example,
$$y\in f(A)=\{f(x) \mid x\in A\} \\ ​​\iff \exists\,y, y=f(x)\land x\in A$$

Answer 1

Your second row is wrong. Rather than $$ (\exists y)\ y = f(x) \text{ and } x\in A $$ It should say $$ (\exists x)\ y = f(x) \text{ and } x\in A. $$