Under the natural partial exchangeability assumption for multi-class interacting particle systems, we prove that these converge to an independent system with infinite i.i.d. classes if and only if the empirical measure of each class satisfies a weak law of large numbers. This extension of a classical result for exchangeable systems (related to the de Finetti Theorem) is somewhat surprising, since then convergence of each class to infinite i.i.d. particles implies asymptotic independence of particles of different classes.