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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. In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both is the inference from the truth of " A implies B" the truth of " Not- B implies not- A", and conversely.
It is very closely related to the rule of inference modus tollens. Quick links Teach Yourself Logic : A Study Guide ( find it on by preference, or here) Appendix: Some Big Books on Mathematical Logic ( pdf) Book Notes ( links to 35 book- by- book webpages, the content overlapping with the Appendix) In more detail, on TYL Most.