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It's not going to rub more, if anything it will be less rubbing. Width of the rim is not relevant because no one in the right mind would mount a tire that is narrower than the rim...you'll have an exploded tire real quick if you do that. Think of it this way, the widest part of your tire on both sets is 245mm so with a smaller rim and less sidewall, your overall diameter on the 18's is going to be smaller than the 20's so you should be ok. Why won't you ask the guy to bring one over to you to test fit it to be certain?
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