Let $(W_t)_{t\ge 0}$ be a 2-dimensional Brownian motion on some filtered probability space and $x \in \mathbb R^2$. Further define $\tau_x:=\{t >0 \,:\, W_t=x\}$ the hitting time of the singleton $x$.
I know that it holds $$\mathbb P \left(\tau_x < \infty \right)\; = \; 0$$
Yet, I was wondering if there is a rather simple proof of this property?
Thank you a lot in advance!