A Stronger Result than Grauert-Narasimhan's Solution to Levi Problem

In this note, we'll establish the following Main Theorem. Let D be a locally finite intersection of bounded strictly pseudoconvex domains in a complex space. Then there exists a proper holomorphic mapping f from D into some unit ball. This result is stronger than Grauert-Narasimhan's solution to Levi problem. Our proof is based on a theorem in [10], and other known results. This note may be regarded as a continuation of [10]. Prof. H. Grauert told me that the present result was an open problem before we prove it.