Exercise 2, § 4

Let $A$ and $B$ be relations in $\mathscr{T}$, and let $x$ be a letter, distinct from the constants of $\mathscr{T}$, which does not appear in $A$. If $B \Rightarrow A$ is a theorem in $\mathscr{T}$, then $((\exists x)B) \Rightarrow A$ is a theorem in $\mathscr{T}$.