Why we are sure that the presentation for the braid group is
$$ \mathcal{B}_n= \left\langle \sigma_1 , \dots, \sigma_{n-1} \vert \mathcal{R}_n \right\rangle, $$
where $$\mathcal{R}_n=\left\{ \begin{smallmatrix} \sigma_i\sigma_{i+1}\sigma_i=\sigma_{i+1}\sigma_i\sigma_{i+1} \ \forall \ 1\leq i\leq n-2, \\ \sigma_i\sigma_j = \sigma_j\sigma_i \ \mbox{if } \vert i-j\vert \ge 2 \end{smallmatrix} \right\}$$
How can we prove it? It's obvious that those relations are true in the Braid Group, but how we know that those are the unique relations needed?
The definition I'm basing is the group of isotopy classes of braids of $n$ strands.