Definition:Substitution (Formal Systems)/Metasymbol

Definition

Let $S_1$ be a statement form.

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

Let $T$ be a statement.

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

Then $S_2$ results from the substitution of $p$ by $T$ in $S_1$.

$S_2$ is called a substitution instance of $S_1$.

1964: Donald Kalish and Richard Montague: Logic: Techniques of Formal Reasoning ... (previous) ... (next): $\text{II}$: 'AND', 'OR', 'IF AND ONLY IF': $\S 4$
1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $2$: Theorems and Derived Rules
1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.3$: Argument Forms and Truth Tables
1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 3$: Logical Constants $(2)$