Existential instantiation
In predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form , one may infer  for a new constant symbol c. The rule has the restrictions that the constant c introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof. It is also necessary that every instance of  which is bound to  must be uniformly replaced by c. This is implied by the notation , but its explicit statement is often left out of explanations. In one formal notation, the rule may be denoted by

where a is a new constant symbol that has not appeared in the proof. See also 
 Existential fallacy
 Universal instantiation
 List of rules of inference

References 

Rules of inference
Predicate logic