Exactly.
Back in HS (1993-1997) I put on about 20 lbs of muscle a year (went from 125 as a frosh to 190 as a senior, all muscle gain, I wasn't any taller) all by just eating a bunch of protein, carbs, and lifting my ass off (heavy weights, small reps).
I started doing it again recently (just started working out 2 months ago) I have lost almost 3 inches on my waist but have actually gained weight and my belly has significantly gone down (really only some love handles left I am working on). This is all just by doing some cardio (15-25 minutes) and lifting my ass off afterwards.
In 2 months I have gone from doing sets of just 135 lb on the bench to sets of 225 (most of that gain was getting some shoulder muscles stabilized as I broke my shoulder 2 years ago and never rehabbed it correctly).
I literally went from a 'gut' to a 6 pack in less than 2 months, amazing what just lifting your ass off will do.
The best part is that me hitting the gym hard for a couple months has motivated my wife to do so as well, and she has lost 15 lbs in a month (some cardio and low weight/high rep weight training). She is addicted to exercise now and she has never really been to the gym before this.