substitution-instance

In logic, a substitution instance is a statement derived from a statement form by replacing variables with specific constants. This concept is fundamental in formal logic, particularly in the predicate calculus, where formulas are constructed using individual variables (like x, y) and predicate variables (like φ, ψ).12

For example, if you have a statement form like φx (meaning "x has property φ"), a substitution instance would be "Socrates is wise" if φ is replaced by "is wise" and x is replaced by "Socrates". This process allows for the creation of specific propositions from general logical structures. Combinatory logic also deals with substitution and the elimination of variables using special function symbols.23