 Theophrastus claimed that certain prosleptic premises were equivalent to categorical propositions; for instance, “A holds of all of that of all of which B holds” is equivalent to “A holds of all B”. Nevertheless, since there are prosleptic premises that are not equivalent to categorical propositions, many prosleptic syllogisms cannot be reduced to categorical syllogisms (see Lejewski 1961, 1976; Kneale and Kneale 1972).