Proving the invalidity arguments in quantifier logic.

Question

I am studying how to prove an argument in quantifier logic is invalid. The textbook I am using by Virginia Klenk claims that you can use a Model Universe that contains a finite number of objects to substitute in to the propositional functions. The book claims: "Where n is the number of different predicate letters in an argument form, the largest domain you need to test is one with $2^n$ individuals." Can someone explain or refer me to a proof for why this is so?