Exercise 7, § 4

Let $A$ and $R$ be relations in $\mathscr{T}$, and let $x$ be a letter distinct from the constants of $\mathscr{T}$. If $R \Rightarrow A$ is a theorem in $\mathscr{T}$, then

is a theorem in $\mathscr{T}$. If (not $R$) $\Rightarrow A$ is a theorem in $\mathscr{T}$, then

is a theorem in $\mathscr{T}$. In particular, if $A$ is a theorem in $\mathscr{T}$,

are theorems in $\mathscr{T}$.