Definition:Substitution Instance

Propositional Logic
Let $S_1$ be a statement form of propositional logic.

Let $p$ be a statement variable which occurs one or more times in $S_1$.

Let $T$ be a statement form of propositional logic.

Let $S_2$ be the string formed by replacing every occurrence of $p$ in $S_1$ with $T$.

Then $S_2$ is a substitution instance of $p$ by $T$ in $S_1$.

Propositional Calculus
In the context of mathematical logic and the development of propositional calculus as a formal system, this definition can be expressed as.

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

Let $p$ be a proposition symbol which occurs one or more times in $\mathbf A$.

Let $\mathbb B$ be a statement form of propositional logic.

Let $\mathbb C$ be the string formed by replacing every occurrence of $p$ in $\mathbf A$ with $\mathbb B$.

Then $\mathbb C$ is a substitution instance of $p$ by $\mathbf B$ in $\mathbf A$.

Also known as
Some sources hyphenate: substitution-instance.

Also see

 * Rule of Substitution