Absorption / modus tollens / modus ponendo tollens
Negation introduction
Rules of replacement
Associativity
Commutativity
Distributivity
Double negation
De Morgan's laws
Transposition
Material implication
Exportation
Tautology
Predicate logic
Rules of inference
Universal generalization / instantiation
Existential generalization / 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.
In one formal notation, the rule may be denoted by
where a is a new constant symbol that has not appeared in the proof.
^Hurley, Patrick. A Concise Introduction to Logic. Wadsworth Pub Co, 2008.
^Copi and Cohen
^Moore and Parker
and 27 Related for: Existential instantiation information
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