Well-Ordering Principle/Proof using Von Neumann Construction

Proof
From Von Neumann Construction of Natural Numbers is Minimally Inductive, $\omega$ is minimally inductive class under the successor mapping.

From Successor Mapping on Natural Numbers is Progressing, this successor mapping is a progressing mapping.

The result is a direct application of Minimally Inductive Class under Progressing Mapping is Well-Ordered under Subset Relation.