eating bad food leads to type 2 diabetics

It is 10:50 am and I am watching "Everyday History" on the Discovery Channel; they are doing a story about UFOs. I was reading through my diabetes blog material and was thinking about a black family I saw in the late 1960s. This family (Dad, Mom and Daughter) worked at the Keesler Air Force Base theater popcorn stand in Biloxi Mississippi. They were a curiosity because they were quite fat. (That was in the late 1960s; I don't know that they are diabetics but I'd be surprised it they were not!)

My Mother said they were so fat because they could not afford good (healthy) food.

I have  since learned that being fat is generally a prime prerequisite for type two diabetes. By the logic of

if A ⇒ B and B ⇒ C then A ⇒ C

Apply this logic and you get:

if eating bad food ⇒ obesity and obesity ⇒ type 2 diabetes

then

eating bad food ⇒ type 2 diabetes

Assuming my premises are correct and the form of the logic chain is correct (it is!) then I have just logically proven that eating the wrong food leads to type 2 diabetes.

NOTE: The character ⇒ is "implies".