  The conditions for proper definitions in mathematics are given, in terms of
the theory of definition, on the basis of the criterions of eliminability and
non-creativity. As a definition, Russell's antinomy is a violation of the
criterion of eliminability (Behmann, 1931; Bochvar, 1943). Following the path
of the criterion of non-creativity, this paper develops a new analysis of
Comprehension schema and, as a consequence, proof that Russell's antinomy
argumentation, despite the words of Frege himself, does not hold in
Grundgesetze der Arithmetik. According to Basic Law (III), the class of classes
not belonging to themselves is a class defined by a function which can not take
as argument its own course of value. In other words, the class of classes not
belonging to themselves is a class whose classes are not identical to the class
itself.
