The articles [12], [8], [13], [11], [14], [5], [4], [9], [16], [1], [2], [7], and [6] provide the notation and terminology for this paper. Let X be a set and let Y be a subset of 2X . Then ⋃ Y is a subset of X . In this article we present several logical schemes. The scheme DenestFraenkel deals with a non empty set A , a non empty set B, a unary functor F yielding a set, a unary functor G yield...