# 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.