reserve v for object;
reserve V,A for set;
reserve f for SCBinominativeFunction of V,A;

theorem Th3:
  A is_without_nonatomicND_wrt V implies
  for d being NonatomicND of V,A holds not d in A
  proof
    assume
A1: A is_without_nonatomicND_wrt V;
    let d be NonatomicND of V,A;
    d in nonatomicsND(V,A);
    hence thesis by A1,XBOOLE_0:3;
  end;
