surjective open maps in terms of nets

Theorem - Let $f:X⟶Y$ be a surjective map between the topological spaces $X$ and $Y$. Then $f$ is an open mapping if and only if given a net ${\{y_i\}}_{i\in I}\subset Y$ such that $y_i⟶y$, then for every $x\in f^{-1}(\{y\})$ there exists a subnet ${\{y_{i_j}\}}_{j\in J}$ that