We show transience of the edge-reinforced random walk for small reinforcement in dimension $d\ge3$. The argument adapts the proof of quasi-diffusive behaviour of the SuSy hyperbolic model for fixed conductances by Disertori, Spencer and Zirnbauer (2010), using the representation of edge-reinforced random walk as a mixture of vertex-reinforced jump processes (VRJP) with independent gamma conductances, and the interpretation of the limit law of VRJP as a supersymmetric (SuSy) hyperbolic sigma model developed by Sabot and Tarres (2012).
