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How do complex propositions and Aristotle's logic work?

Is it allowed to create a syllogism with complex propositions? Here is my example where P is a sequence of actions and M is a final cause. S = "Cake maker" P = "Finding of ingredients, ...
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Is this Barbara syllogism of a final cause right?

Hi i'm trying to learn how to make an explanation of a final cause in the form of a Barbara syllogism but I don't know if I have the terms in the right order. The Barbara definition I'm using is from ...
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