Coordinate projections from arbitrary products are open maps

Let \(\{X_\alpha\}_{\alpha\in I}\) be topological spaces and give \[ \prod_{\alpha\in I}X_\alpha \] the product topology. For every \(\beta\in I\), prove that the coordinate projection \[ \pi_\beta:\prod_{\alpha\in I}X_\alpha\longrightarrow X_\beta \] is an open map.