Existential instantiation

In predicate logic, existential instantiation (also called existential elimination)[1][2][3] 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.

Existential instantiation
TypeRule of inference
FieldPredicate logic
Symbolic statement

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

References

  1. Hurley, Patrick. A Concise Introduction to Logic. Wadsworth Pub Co, 2008.
  2. Copi and Cohen
  3. Moore and Parker
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