I need a proof of this well known fact:
If a group $G$ is given as a quotient of a free group $F/R$ then its pro-finite completion is given by the quotient $\hat{F}/ \bar{R}$ where $\bar{R}$ is the closure of $R$ in $\hat{F}$. (since $F$ embeds into $\hat{F}$ densely we can think of $R$ inside $\hat{F}$)
Thanks in advance.