Is is bad to feel like I'm smarter than other people because I go to a prestigious college?

I attend a prestigious university (one of the top 20 in the nation). I am very proud of this fact because I worked very hard to get in. I am not rich, by the way, I'm here on an academic scholarship. My high school friends went to schools all over the country, but none as highly ranking as mine. Is it bad that I secretly feel smarter than them, and consequently a little better than them, because of this fact? I never say this out loud or brag about my college at all, but every time I get that secret feeling that I'm better than them, I feel guilty.