Redirecting sub-domain blog to root-domain's subfolder hurts the traffic of old blogs?

We have done a reverse proxy to forward blog.casefox.com to casefox.com/blog/. As I think it gives great help in getting the “link juice” to the root domain.

However, I am concerned about any possibility of harm to the existing SEO value of the blog. Is there any way to not lose the traffic of the old blogs and reverse proxy doesn’t hurt website traffic/juice?

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