\begin{definition}[Definition:Relative Semantic Equivalence/WFF]
Let $\FF$ be a theory in the language of predicate logic.
Let $\mathbf A, \mathbf B$ be WFFs.
Let $\mathbf C$ be the universal closure of $\mathbf A \iff \mathbf B$.
Then $\mathbf A$ and $\mathbf B$ are '''semantically equivalent with respect to $\FF$''' {{iff}}:
:$\FF \models_{\mathrm{PL}} \mathbf C$
That is, {{iff}} $\mathbf C$ is a semantic consequence of $\FF$.
\end{definition}