This discussion illustrates an interesting point -- it can be a little tricky to judge whether two proofs are actually &quot;different&quot; or not.<p>When I was a grad student I interrupted a study session to raise the simple question -- can a theorem really have two different proofs? We all thought the answer was yes, but the discussion went on for several minutes until I settled it by contriving a stupidly simple and synthetic set of axioms to construct a example.<p>Basically, the axioms were:<p>&quot;All As are also Bs&quot;
&quot;All As are also Cs&quot;
&quot;All Bs are also Ds&quot;
&quot;All Cs are also Ds&quot;<p>and the theorem was<p>&quot;All As are also Ds&quot;