When a form of logical statement that implies existence is derived from premisses in which existence is not necessarily implied, existence must first be proven.
All giant squids are deep-sea animals.
[and giant squids exist.]
There exist giant squids that are deep-sea animals.
“Giant squid” refers to several species of invertebrates that were long thought to be merely sailor’s yarn, i.e. some kind of mythical sea-monsters. Their existence has only been proven during the 20th century.
This proof of existence is required in order to be able to derive an existential statement (which does require existence) from a universal one (which does not require it).
A recurring issue in the validity of logical statements concerns the question of existence of the objects that the terms actually refer to. There are certain statements that are valid even if (or even because) they refer to an empty extension of a term.
For example, all universal statements (like “all A are B”) are valid even if the extension of their antecedents might be empty. In fact, if we know that it is empty, it is even guaranteed to be true (☞ vacuous truth). On the other side, existential statements (e.g. “some A are B”) require that the terms refer to something that actually exists (hence the name).
For this reason, the syllogism forms in which an existential conclusion is derived from one or multiple universal premisses require that the existence of certain terms is proven in order to be valid. This affects the syllogistic modi Barbari, Bamalip, Calemos, Camestros, Celaront, Cesaro, Darapti, Felapton and Fesapo.
In the example above, the existential import is made explicit by inserting a new premise. In other situation, this may be done implicitly (☞ enthymeme). Generally, it is to be preferred to do this explicitly, however, as this can help to avoid the so-called “existential fallacy”.