A statement has existential import if its truth depends on the
existence of objects of a certain type.
For modern predicate logic, universal statements necessarily lack
existential import. Because they are conditionals, they do not
assert the existence of any Ss; all they say is that if any x is
an S, then it is (or is not) a P.
If there are no Ss, then any statement of the form (x) (Sx ...) is true by default, regardless of the consequent, because the
antecedent is not true of anything. That follows from the nature
of conditionals as defined by the truth table.
By contrast, particular statements do have existential import. By the nature of conjunction, any statement of the form (x) (Sx
. ...) is true only if some x is S.