equivalence between the minor and topological minor of $K_5$ or $K_{3,3}$

A graph $G$ contains $K_5$ or $K_{3,3}$ as a minor iff it contains $K_5$ or $K_{3,3}$ as a topological minor (http://planetmath.org/subdivision). Where $K_5$ is the complete graph of order 5 and $K_{3,3}$ is the complete bipartite graph of order 6.

Remark that this theorem shows that Wagner’s theorem and Kuratowski’s theorem are equivalent.