  Recently, Todorov and Wilf independently realized that de Branges' original
proof of the Bieberbach and Milin conjectures and the proof that was later
given by Weinstein deal with the same special function system that de Branges
had introduced in his work.
  In this article, we present an elementary proof of this statement based on
the defining differential equations system rather than the closed
representation of de Branges' function system. Our proof does neither use
special functions (like Wilf's) nor the residue theorem (like Todorov's) nor
the closed representation (like both), but is purely algebraic.
  On the other hand, by a similar algebraic treatment, the closed
representation of de Branges' function system is derived. In a final section,
we give a simple representation of a generating function of the de Branges
functions.
