A short and elementary proof of Hanners theorem

Hanners theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanners original proof of the theorem is quite simple for separable spaces, it is rather involved for the general case. We provide a proof which is not only short, but also elementary, relying only on well-known classical point-set topology.