An essential predication (predication of the Essence or part thereof) cannot be proved, because the term standing for that Essence must be the middle term, for in the minor must be placed the definition of the subject, but then we have a petitio principii (Aristotle, II Posteriora Analytica, Cap.4) : On the basis of the definition of the subject (that is, departing from the definition of the subject) we should, in the course of the argument, come to know more about that subject. This 'more' is then predicated of the subject in the conclusion, and (this 'more') was already conceded in the 1st premise wit respect to a broader class. The Essence cannot be proved as being the essence of the given subject, because the Essence must be stated in the definition of the subject which means that the conclusion is already contained in at least one of the premises.
Predication of an accidental content (that is, a formal content that can per accidens find itself to be connected to the subject, while it does not necessarily belong to that subject) can also not be proven (demonstrated), because also one of the premises is con-tingent, rendering the demonstration conditional :
Some animals have bones (which could be rephrased as ' Some animals are boned ' )
A frog is an animal
Conclusion : A frog may have bones
Some animals have bones
A fly is an animal
Conclusion : A fly may have bones.
So only the ' being-in ' of a proprium can be proved for that what is subsumed under that class (of things) for which it is a proprium.