7.2.4 Universal introduction

Well, this one is easy:

$$\begin{fitch*} \par n & A \\ \par \hline \par & \forall x A & I$\forall$\ n \par \end{fitch*}$$

So, if we know that $A$ is always true, then it is true for any value of $x$. No free $x$ should appear in any attainable hypothesis.