Cauchy-Riemann equations?

They Cauchy-Riemann equations are ux (x,y) = vy (x,y) and uy (x,y) = -vx (x,y). Suppose that u and v have continuous derivatives of the first and second order on domain D and that u and v satisfy the Cacuhy-Riemann equations. Prove that u and v are both harmonic, i.e. they both satisfy the Laplace equation uxx + uyy = 0.