  Given a reduced analytic space $Y$ we introduce a class of {\it nice} cycles,
including all effective $\mathbb{Q}$-Cartier divisors. Equidimensional nice
cycles that intersect properly allow for a natural intersection product. Using
$\bar{\partial}$-potentials and residue calculus we provide an intrinsic way of
defining this product. The intrinsic definition makes it possible to prove
global formulas. In case $Y$ is smooth all cycles are differences of nice
cycles, and so we get a new way to define classical proper intersections.
