This is not a proof (of money having value per se). Though I was hoping that you would address the issue that I raised in my post (since that would be a proof). I mean, the compliance (or lack thereof) between the notion of money having value as such and the law of diminishing marginal utility...
It is proof. Value is somebody prefering one thing over the other.
We could go on discussing the two types of value again, but this time I wanted to stress that money is value.
So you don't want to address the issue of the discrepancy that I pointed out, okay then. Would money have value to you if you could buy with it only things that you don't need (and couldn't barter with) and, consequently, couldn't that you do? I guess that it wouldn't. Therefore it is not money per se that has value but the value of things that you can buy with it, and only through these things that actually satisfy your needs money obtains its value...
And this pretty much explains the apparent contradiction between the law of diminishing marginal utility and money not conforming to it. If you still disagree, then you have to explain this non-conformance somehow