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

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Let $\FF$ be a formal language with alphabet $\AA$.

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

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

Then $\mathbf B$ is a proper well-formed part of $\mathbf A$ if and only if $\mathbf B$ 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.