Definition:Substitution (Formal Systems)/Well-Formed Part

Definition
Let $\mathbf B$ be WFFs of propositional logic, and let $\mathbf A$ be a well-formed part of $\mathbf B$.

Let $\mathbf A'$ be another WFF.

Then the substitution of $\mathbf A'$ for $\mathbf A$ in $\mathbf B$ is the WFF resulting from $\mathbf B$ by replacing all occurrences of $\mathbf A$ in $\mathbf B$ by $\mathbf A'$.

It is denoted as $\mathbf B \left({\mathbf A \,//\, \mathbf A'}\right)$.

Also denoted as
There are many alternative notations for $\mathbf B \left({\mathbf A \,//\, \mathbf A'}\right)$.

These mainly concern the style of the brackets, and sometimes an alternative symbol (usually $\gets$) for the slashes $//$.

For example:


 * $\mathbf B \left\{{\mathbf A \gets \mathbf A'}\right\}$
 * $\mathbf B \left[{\mathbf A \,//\, \mathbf A'}\right]$