  We present a new and simple proof of Teichm\"uller-Wittich-Belinskii's and
Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at
a given point. Known proofs gave separate estimates for the radial and angular
variations, but our proof unifies them using Gr\"otzsch-type inequality for the
variation of cross-ratio of four points on the Riemann sphere. We also give a
sufficient condition for $C^{1+\alpha}$-conformality
