Universal instantiation

In predicate logic universal instantiation (UI, also called universal specification or universal elimination, and sometimes confused with Dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom. It is one of the basic principles used in quantification theory.

Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal."

In symbols the rule as an axiom schema is

for some term a and where ${\displaystyle A(a/x)}$ is the result of substituting a for all occurrences of x in A. ${\displaystyle \,A(a/x)}$ is an instance of ${\displaystyle \forall x\,A(x).}$

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