定理 4 辖域的扩展或收紧
设 $B$ 不含变元 $x$，或与变元 $x$ 无关，则
\begin{equation}
\begin{aligned}
\forall x (A(x) \lor B) &\Leftrightarrow (\forall x A(x)) \lor B, \\
\forall x (A(x) \land B) &\Leftrightarrow (\forall x A(x)) \land B ~.
\end{aligned}
\end{equation}
且
\begin{equation}
\begin{aligned}
\exists x (A(x) \lor B) &\Leftrightarrow (\exists x A(x)) \lor B, \\
\exists x (A(x) \land B) &\Leftrightarrow (\exists x A(x)) \land B ~.
\end{aligned}
\end{equation}