Does this one-line proof qualify? $$1={\rm Pf}\,\Omega={\rm Pf}\, (M^T \Omega M) = ({\rm Det}\,M)\,({\rm Pf}\,\Omega)={\rm Det}\,M,$$ where I have used the defining property $M^T \Omega M=\Omega$ with $\Omega={{0\;\;I}\choose{-I\;0}}$.