As many people pointed out here, copying proof of well-known results is not a new problem. Just that whatever it took days to do it in the pre-Internet age would only take minutes today.
My suggestion is to improve the way you grade the student's homeworks. When you give them the problems, you tell them to give you step by step detail proofs. The solutions they can find on Internet usually are not detailed enough. You can tell from the sheets they submitted whether they absorbed the answers and re-wrote them in full details or simply straight copying.
Many years ago (stone age), I took a graduate math class. I found some homework problems in the Schaum's series book, I copied the answers. I got a C grade back. I went to the professor to ask what was wrong. He showed me his Schaum's book. Next time, I took time to re-write the answer to the extent that he knew I did spend efforts. I got A.
