At first glance, that looks good. But what is a well-ordered set? It is a set that has a well-order. But in general, a well-ordered set has many well-orders. So for each set you can't first just say "pick the least element" you first have to pick a well-order, then you can choose the least element. But the problem of picking a well-order for each set is tricky in itself. I have to think on how you'd do this.