In predicate logic, existential generalization (also known as existential introduction, ∃I) 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." Example: "Alice made herself a cup of tea. Therefore, Alice made someone a cup of tea." Example: "Alice made herself a cup of tea. Therefore, someone made someone a cup of tea." In the Fitch-style calculus: where is obtained from by replacing all its free occurrences of (or some of them) by . 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. See also Inference rules References Rules of inference Predicate logic