Is iTunes still authorized on a computer that I uninstalled iTunes from?

I know this sounds like a stupid question, but I wanted to make sure since I have an iPhone, and I used to buy songs and stuff on my mother's computer. iTunes used to be on her laptop too, but I deleted it from there before I moved in for college. I downloaded iTunes on my laptop that I brought with me on campus, and when I authorized it, it said iTunes was authorized on three out of five devices. Does this include my iPhone as well, or did I do something improperly to the laptop I deleted iTunes from?