Uniform Kazhdan constant for some families of linear groups

Let R be a ring generated by l elements with stable range r. Assume that the group ELd(R) has Kazhdan constant 0>0 for some d r+1. We prove that there exist ( 0,l)>0 and , s.t. for every n d, ELn(R) has a generating set of order k and a Kazhdan constant larger than . As a consequence, we obtain for where n 3, a Kazhdan constant which is independent of n w.r.t. generating set of a fixed size.