Starting with the rigorous expressions, derived previously for the generalized transport coefficients of a multi-component fluid, we obtained several exact relations for partial conductivities of ionic charge-asymmetric mixtures. For a simpler case of a charge-symmetric binary mixture such kind of relations was discovered experimentally by Sundheim more than 50 years ago and is known as the "universal golden rule". Some more complicate models, describing in particular the cases of ternary and multi-component mixtures, are considered. The general relation for partial ionic conductivities is derived for a multi-component ionic fluid. It is shown that such relations can be considered in fact as an example of a more general class of rigorous expressions valid for (k,ω)-dependent quantities.