The opposite. There is plenty of SEO benefit to syndicating.
So long as the syndicated post points directly back to the post's original location (i.e., your blog), you're in good shape. You're getting one-way links and (hopefully) keyword-rich anchor text.
From the Google webmaster blog (http://googlewebmastercentral.blogsp...content.html):
"Syndicate carefully: If you syndicate your content on other sites, make sure they include a link back to the original article on each syndicated article. Even with that, note that we'll always show the (unblocked) version we think is most appropriate for users in each given search, which may or may not be the version you'd prefer."

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