Question with Predicate logic

I have the question: "Translate the following argument into the language of predicate logic. Determine if it is valid or invalid. Justify your answer by providing either an interpretation or a proof. All babies are illogical and nothing that is despised can manage a crocodile. Not all illogical things are despised, therefore some baby can manage some crocodile."

I have it translated in a way that I think is correct with $$(∀x~(Bx → Ix) ∧ ∀y~(Mc → ¬Dy)) , \\(∃x~(Ix → Dx))\\ \therefore~(∃x~(Bx → Mc))$$

I am trying to go through with a proof and I have not solved it, I keep on getting stuck while attempting it. Any help with forming a proof or an interpretation that proves it's validity would be greatly appreciated.

• Your "translation" would be easier to follow if you explained what the predicate symbols stand for. – hardmath Dec 5 '18 at 4:39