Let z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w = f(z) mapping R one-to-one onto the disk left bracketing bar w right bracketing bar <1 such that f(z_0) = 0 and f'(z_0)>0. The corollary guarantees that any two simply connected regions except R^2 (the Euclidean plane) can be mapped conformally onto each other.