  G. L\"uders and W. Pauli proved the $\mathcal{CPT}$ theorem based on
Lagrangian quantum field theory almost half a century ago. R. Jost gave a more
general proof based on ``axiomatic'' field theory nearly as long ago. The
axiomatic point of view has two advantages over the Lagrangian one. First, the
axiomatic point of view makes clear why $\mathcal{CPT}$ is fundamental--because
it is intimately related to Lorentz invariance. Secondly, the axiomatic proof
gives a simple way to calculate the $\mathcal{CPT}$ transform of any
relativistic field without calculating $\mathcal{C}$, $\mathcal{P}$ and
$\mathcal{T}$ separately and then multiplying them. The purpose of this
pedagogical paper is to ``deaxiomatize'' the $\mathcal{CPT}$ theorem by
explaining it in a few simple steps. We use theorems of distribution theory and
of several complex variables without proof to make the exposition elementary.

High Energy Physics - Phenomenology;High Energy Physics - Theory;Nuclear Theory