Existential generalization


In predicate logic, existential generalization is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier in formal proofs.
Example: "Rover loves to wag his tail. Therefore, something loves to wag its tail."
In the Fitch-style calculus:
Where replaces all free instances of within.

Quine

According to Willard Van Orman Quine, universal instantiation and existential generalization are two aspects of a single principle, for instead of saying that implies, we could as well say that the denial implies. The principle embodied in these two operations is the link between quantifications and the singular statements that are related to them as instances. Yet it is a principle only by courtesy. It holds only in the case where a term names and, furthermore, occurs referentially.