Assume that weak existence holds for $\mathcal{E}(\sigma, b)$ and that pathwise uniqueness holds. Then:
1. Uniqueness in law holds.
2. For every filtered probability space $(\Omega, \mathcal{F}, (\mathcal{F}_t), \mathbb{P})$ satisfying the usual conditions, every $(\mathcal{F}_t)$-Brownian motion $W$, and every $x \in \mathbb{R}^d$, there exists a unique strong solution to $\mathcal{E}_x(\sigma, b)$.