Let $\mathbf{A}$ and $\mathbf{C}$ be wffs and let $\mathbf{m}$ be a propositional variable such that $\mathbf{C}$ is free for $\mathbf{m}$ in $\mathbf{A}$. Let $\mathbf{x}_1, \ldots, \mathbf{x}_n$ be the free individual variables of $\mathbf{C}$, and let $\mathbf{u}_1, \ldots, \mathbf{u}_n$ be distinct individual variables which do not occur in $\mathbf{C}$ or $\mathbf{A}$. examples to illustrate this metatheorem, and to show the necessity of various conditions in its hypotheses.