Exercise 8, § 4

Let $A$ and $R$ be relations in $\mathscr{T}$, let $T$ be a term in $\mathscr{T}$ and let $x$ be a letter. If $(Tx|)A$ is a theorem in $\mathscr{T}$, then $(T|x)R \Rightarrow (\exists_A x)R$ and $(\forall_A x)R \Rightarrow (T|x)R$ are theorems in $\mathscr{T}$.