The dependence of things as being appearances is not their dependent origination, it is simply their appearance.
That is, dependent origination, is Void, it's not an object of perception. There is nothing out there that is connected in any way; their appearance is based on them being dependent on each other – we can't have fingers if we don't have a hand, and vice versa. But that's all they are as objects.
The reason for establishing the dependence of things, is for explaining their appearance, which is all they are as objects. If we take away their appearance, there is nothing left in its place, and since everything is defined in relation with everything else, everything must go with it.
But their dependent origination is NOT their dependence, since it's not a phenomena, it is their VOIDNESS as being the phenomenal entities that we assume them to be.
Their voidness is not due to the fact that they are dependent, since their dependence is all that they have ever been as appearance (which is how we know them).
We look at a chair and say: ”that's a chair”, and why? Because it is of so an so height, and that you can sit on it, and it has four legs, and so on. This ”dependence” of different attributes is not what makes it void, it's what makes it an object at all, as an appearance – because that is all we know of it (its legs, its height, etc).
Since dependent origination is not a phenomenon we cannot give it a definition, either (without making it an object, of course).