There exists in the context of "Uniqueness quantification"

In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. This sort of quantification is known as uniqueness quantification or unique existential quantification, and is often denoted with the symbols "∃!" or "∃₌₁". It is defined to mean there exists an object with the given property, and all objects with this property are equal.