Is the Proof Behind Choosing Any Point on an Axis to Calculate Torque?

[Ajaysabarish97]

I know that to calculate the torque about an axis, we can choose any point on that axis and find the torque about that point and take the component along the direction of the axis.Buy what is the proof behind this theorem?

 

[andrewkirk]

Split the torque into two components, one parallel to the axis and the other orthogonal to it. Then the second one is trying to change the orientation of the axis and so will be resisted by an equal and opposite torque applied by whatever structures hold the axis in place, such as bearings and wheel struts. When we add in that reactive torque, we are left with the component parallel to the axis.