Stopping of quadratic covariaton

Question

I am given two local martingales $M$ and $N$ and a stopping time $\tau$. We work on a finite time interval $[0,T]$. I want to prove $$\langle M,N\rangle^{\tau}=\langle M^\tau,N\rangle$$ using the uniqueness of the process $\langle M,N\rangle$ among all continuous, adapted processes of finite variation such that $MN-\langle M,N\rangle$ is a local martingale. (The superscript $\tau$ just indicates the stopped process.) Can someone give me a hint how I could find a proof? Thanks a lot!