Definition:Well-Formed Part/Proper Well-Formed Part

Definition
Let $\mathcal F$ be a formal language with alphabet $\mathcal A$.

Let $\mathbf A$ be a well-formed formula of $\mathcal F$.

Let $\mathbf B$ be a well-formed part of $\mathbf A$.

Then $\mathbf B$ is a proper well-formed part of $\mathbf A$ iff $\mathbf B$ is not equal to $\mathbf A$.

Also known as
In sources where WFFs are referred to as formulas, the term proper subformula can often be seen.