Proving $\{xx^R \mid x\in L_1, x^R\in L_2\}$ is context-free I have this problem:


  Let $L_1$ and $L_2$ be two regular languages.  Show that $L_3 = \{xx^r : x \in L_1, x^r \in L_2 \}$ is a context-free language.


I am unsure how to prove that some language is context-free. Could someone please provide the steps?
One way to prove that a language is context-free is to find a context-free grammar that recognizes it. Just go through the definition (on Wikipedia for example) and try to find a context-free grammar for $L_3$ (it's easy). Good luck!