  The moving lemma of Suslin states that a cycle on $X\times \mathbb{A} ^n$
meeting all faces properly can be moved so that it becomes equidimensional over
$\mathbb{A}^n$. This leads to an isomorphism of motivic Borel-Moore homology
and higher Chow groups.
  In this short paper we formulate and prove a variant of this. It leads to an
isomorphism of Suslin homology with modulus and higher Chow groups with
modulus, in an appropriate pro setting.
