For example, I have two points A and B, and I can prove that the electric field produced by a point charge sitting at A is irrotational with respect to the spherical polar coordinate system that has its origin at A. If I express the electric field of said charge, which sits at point A, with respect to the spherical polar coordinate system that has its origin at B and calculate the field's curl, will I find that the curl in this system is also zero?
(I know physics says "any electrostatic field is irrotational", I'm just trying to figure out whether or not that can be proved mathematically using the above argument)