I think 'law' is too strong of a word, though I confess I've used it as an explanatory phrase myself. I think the basic idea is helpful because I believe that the Bible often/largely defines itself, or at least expands on a definition. I'm a huge believer in carefully defining a word/concept when teaching/preaching on it and this is why the 'law' of first mention is helpful. IOW, to me, it isn't about shoehorning OT doctrine/practice into the NT it is about explaining/understanding the thought/meaning behind the word/phrase in the NT.
I have never been able to find that "law" in the Bible. The first time God mentions something, He does not necessarily explain everything about it. This "law" allows a person to reject verses he doesn't like, if they come in later books.