Statics: particle mechanics versus rigid body mechanics

Statics: particle mechanics versus rigid body mechanics

In particle mechanics where the notion of rotation does not apply,
particles are said to be under static equilibrium when the sum of the
forces acting on the particle of interest in all directions equals zero.
In rigid body mechanics where the notion of rotation applies (or at least
the concept of invariant distances between points), rigid bodies are said
to be under static equilibrium when (1) the sum of the forces in all
directions equals zero, and (2) the sum of the moments in all directions
equals zero.
My question is: in rigid body mechanics, where does the equation on
moments come from? Is it a principle similar to Newton's law in particle
mechanics or can it be proven from other assumptions (like, for instance,
the invariance of distances separating two points)