Unique local-name()

I'm really stuck on a XPpath problem that should be fairly simple (I
think): I need to check if an element that got a unique local-name()
among it's siblings. And, I have no way of actually knowing the
local-name() when I generate the XPath.

For example:
<root>
	<a />
	<b />
	<b />
	<c />
	<c />
	<d />
</root>

Thanks!
/niklas