Proving the language of a CFG with this rule [duplicate]

If I want to prove a language (e.g. $ L = \{ z \;|\; z \in \{x,y\}^*\}$ ) correct based on a context-free grammar, how can I do so if there exists a rule in the grammar

$ $ S \rightarrow xS \;|\; yS \;|\; \varepsilon$ $

I know that multiple applications of the rules $ S \rightarrow xS$ and $ S \rightarrow yS$ can lead to any string $ z \in \{x,y\}^*$ , but is there a specific way I can show this? I do not know how to articulate this step into my proof.