Symmetric Group is Generated by Transposition and n-Cycle

Theorem
Let $n \in \Z: n > 1$.

Let $S_n$ denote the symmetric group on $n$ letters.

Then the set of cyclic permutations:
 * $\set {\begin {pmatrix} 1 & 2 \end{pmatrix}, \begin {pmatrix} 1 & 2 & \cdots & n \end{pmatrix} }$

is a generator for $S_n$.