The semicolon is correct, though I’d have used a colon, which I think would be a bit more sophisticated in that sentence.
This is what Allan M. Siegal, former standards editor at The New York Times had to say about a New York subway sign that drew attention for its use of the ever-confusing semicolon.
The sign (instructing riders not to leave their newspapers littering the subway) read:
“Please put it in a trash can; that’s good news for everyone.”
I love that I’m not the only one in this big world that gets so excited about a simple piece of punctuation.