Exercise 4, § 5

Let $R$ and $S$ be relations in $\mathscr{T}$, and let $x$ be a letter which is not a constant of $\mathscr{T}$. If $R$ is functional in $x$ in $\mathscr{T}$, and if $R \Leftrightarrow S$ is a theorem in $\mathscr{T}$, then $S$ is functional in $x$ in $\mathscr{T}$.