Use of "but" after "none"

Question

In the quote below, please see the sentence that begins with the word "None." I have a question about the second half of this sentence. To understand it better, I paraphrased it to "none are so poor with a smile but they are richer for its benefits." I feel that the conjunction but is incorrect because it is not introducing an opposing idea. I think that and would be more preferable. I'm sure that the author knew English better than I do, so my thinking must be wrong. Would you please help me understand why I am wrong?

The value of a smile... It costs nothing, but creates much. It enriches those who receive, without impoverishing those who give. It happens in a flash and the memory of it sometimes lasts forever. None are so rich they can get along without it, and none so poor but are richer for its benefits. It creates happiness in the home, fosters good will in a business, and is the countersign of friends.

—Dale Carnegie (2016), How to Win Friends and Influence People, p. 67, Diamond Pocket Books Pvt Ltd.

chaosintheheadspace · Accepted Answer

The "but" seems to be used in the sense of "without its also being the case that". A second "they" has also been omitted, thus:
and none so poor without its also being the case that [they] are richer for its benefits.
Or to paraphrase even further:
and none so poor that they aren't richer for its benefits.
This use of but is very outdated. Of course the original version of the book is from 1936 and this part of it is supposed to be a poem.

RussellC · Answer

I disagree that none .. but is obsolete. I think that the meaning is along these lines. There would be none, except for the example following. E.g:
None but he were present. None of the food was eatable but the bread and butter.

Use of "but" after "none"

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