By existential instantiation, given the premise , we may derive where is a particular object of the domain:
Note: we cannot select an arbitrary object in but rather it must be an object for which is true. Usually, we have no knowledge of what the actual object is, we only know that it does exist. Since it exists, we can give it a new name, not used anywhere before, say , and continue the derivation. Existential instantiation can be seen as .