Thanks to all who answered me
Yes, I did get a lot of responses from my fellow collectors, but also from AMY for NGC who also wrote me with:
"Yes, you may use the same coin (same cert #) in different sets. As in your example, you may register your 1971 1C proof in your 1971 Proof set and in a Lincoln Cent Proof set.
What you may not do is register the same coin (same cert #) to sets of the same type. In your case, you have registered two (2) 1971 Proof sets. You may not register the same coin to both sets."
Now I have to save up $15k for one of the 2 PCGS 1971 PF 70 DCAM Ikes.....why can't NGC grade one that high? :-)