For two intersecting non-coplanar lines, take the point of intersection as A, and one other point on each line. Since, the lines intersect the three points are not colinear. Therefore, all three are in exactly in one plane. That means each line has two points in that plane, so each line is in that plane, therefore they are coplanar. But this contradicts the assumption that the lines were not coplanar. So, the assumption that non-coplanar lines intersect is wrong.
Therefore, two lines that are not coplanar never intersect.