Let $\phi(p)$ be a formula which contains a variable $p$ and doesn't contain the variable $q$. Let $\phi(q)$ be a formula which is constructed in the following way: Every occurence of $p$ in $\phi(p)$ is replaced with $q$. Prove that if $$\phi(p), \phi(q) \models p \leftrightarrow q $$ then there exists a such formula $\psi$ ( which doesn't conatain $p$ and $q$ ) that $$\phi(p) \models p \leftrightarrow \psi$$
Please hint me because I cannot deal with it. Thanks in advance.