Quote:
Originally Posted by CRGreathouse
One proof was good enough to show that the result was true, but it's common to produce alternate proofs. They may be more elegant, or they may show connections that were obscure in the original.

More importantly, different proofs can use different sets of axioms, in which case they will be applicable in different situations. The simplest example I can think of is multiplicative cancellation (i.e. ab=ac implies b=c) which can be proven in (at least) two very different ways.