In Indian logic, the presence of the middle term in the minor term is called:

The presence of the middle term in the minor term is called paksha-dharmita.

The minor term is the paksha, the locus about which the conclusion is drawn.

The middle term must actually reside as a property in that locus.

On the smoky hill, smoke really belongs to the hill itself.

This being-a-property-of-the-paksha is the first condition of a valid mark.

Its technical name in Indian logic is paksha-dharmita.