We give a new proof of a theorem due to Alain Connes, that an injective factor N of type III1 with separable predual and with trivial bicentralizer is isomorphic to the Araki-Woods type III1 factor R∞. This, combined with the author's solution to the bicentralizer problem for injective III1 factors provides a new proof of the theorem that up to *-isomorphism, there exists a unique injective factor of type III1 on a separable Hilbert space
