Definition:Substitution (Set Theory)

Definition
Let $S$ and $T$ be non-empty sets such that $T$ is not a subset of $S$.

Let:
 * $s \in S$
 * $t \in T \setminus S$

where $\setminus$ denotes set difference.

Let $S'$ be the set defined as:
 * $S' = \paren {S \setminus \set s} \cup \set t$

That is, $S'$ is the set obtained by removing $s$ and replacing it with $t$ which is not in $S$.

The operation of replacing $s$ with $t$ is known as substitution.