According to the rules of syllogisms you can't get a conclusion from two negative premises, but since an O proposition i.e. Some A is not B can be expressed as a I proposition, i.e. Some A is non-B, then isn't this latter form just as much an O as an I?

So you can have the syllogism

(E): No A is B
(O): Some B is non-C

Therefore, Some non-C is not A (O).

Confused!

The syllogism you propose is quite valid, but it is not one intended under the rule you state, because you have in fact changed the minor term from C to non-C and the minor premise from a negative form to a positive one. This is legitimate, no problem.

Something about you (optional) Logician, philosopher

Thanks Avi. Actually, thinking about it, you could also do the same for a universal proposition. So 'No A is B' is equivalent to 'All A is non-B' logically speaking.