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 $(\exists x)\phi (x)$, one may infer $\phi (c)$ 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

$(\exists x){\mathcal {F}}x::{\mathcal {F}}a,$

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

See also

• existential fallacy