Can you prove privilege?
Privilege is often something based on people's experiences. When you're an underprivileged class, people will treat you differently than others for doing certain things and people of the same class can agree that they've also experienced that thing. For instance a lot of people see women having a lot of sex partners worse than men having a lot of sex partners. These experiences are circumstantial so there can't be a full consensus, but you might be able to find proof within yourself by examining how you judge others. Maybe something that can be considered proof is how you can point out representation, or a lack of it, for instance you may find stores selling greeting cards for your sigOth that clearly reference heterosexuality but none for homosexuality. You can also use statistics, that might say for example that black people receive longer prison sentences for the same crimes.
You can point out that someone belongs to a privileged group but that doesn't necessarily reflect their experiences– they could be white but poor. Usually the suggestion is that if they had that one trait flipped, their life would have probably been somewhat harder– they could be black and poor.
There is an exercise I've seen called the privilege walk in which a group of people stands at a line and walks forward or backward based on their experiences without asking what groups they belong to. It has directions like, "please take 2 steps back if you have been the victim of domestic violence," "please step forward if you have been accepted into college." There are a few results on Google for this exercise.