There is an idea that you can prove the premises of an argument by creating valid arguments whose conclusion’s are the premises of the original argument. For example, if I have a 2 premise argument with a conclusion, and I want to prove the premises, I will create two more arguments whose conclusion’s are the premises of my original argument. You can see that this becomes problematic very quickly. This method of proving leads to two things; an infinite regress of arguments (which is impossible) or a circular argument.
So what do we do? I recommend that you introduce axioms. If axioms must exist so we can prove things then certain things need to be true for anything to be true. If these truths are not objective they will not fulfill the consequent of the conditional above. Thus objective truths must exist. QED