I want to show that if every production of the grammar $G$ has the form $uXv \rightarrow u \alpha v$ where $X$ is a variable, $u,v \in (A_{T})^*$ and $\alpha \in (A_{T} \cup A_{N})^*$. Then $L(G)$ is a context-free language.
$A_{T}$: the set of terminals.
$A_{N}$: the set of variables.
I tried to simplify the form of productions and introduce new variables to code some terminals and variables together to transform the productions into context-free productions but I did not succeed. I appreciate any help.