Let $\varphi$ be a propositional formula, defined as a formula containing propositional symbols and connectives only, and let $\psi,\chi$ be propositions. I read the following principle of propositional congruence:$$\models\psi\leftrightarrow\chi\quad\iff\quad\models\varphi(\psi)\leftrightarrow\varphi(\chi)$$where $\models$ means validity in every model.
If $\psi$ is equivalent to $\chi$, substituting each other in a propositional formula produce equivalent propositions, of course, therefore I understand the $\Rightarrow$ implication.
But how do wee see how $\models\varphi(\psi)\leftrightarrow\varphi(\chi)$ implies $ \models\psi\leftrightarrow\chi$? Thank you very much for any answer!