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The Constitution certainly backs it up, as well as the 2nd Amendment.
The inherent rights of Man from GOD, not man's law backs it up.
The only way it is not enforceable is if no MAN backs it up.
Well, the constitution is enforceable, in a way. It can be cited as the basis for asserting a right to a remedy against the government. The DoI lacks that "citable" force. It (the DoI) is not binding on the government, or on any person.
The DoI is really radical. It sets the individual (acting as a group) to be master over the government. I believe the US is unique in all of history in that regard. The experiment has run its course. We're back to the historical norm of the government being the master over the people.