Existential instantiation

In predicate logic, existential instantiation (also called existential elimination) is a valid rule of inference which says that, given a formula of the form ( ∃ x ) ϕ ( x ) , one may infer ϕ ( c ) for a new constant or variable symbol c. The rule has the restriction that the constant or variable c introduced by the rule must be a new term that has not occurred earlier in the proof.

In one formal notation, the rule may be denoted

where a is an arbitrary term that has not been a part of our proof thus far.