
theorem Th10:
  for a,b,c,d,e,n being Integer holds
  (a+b+c+d+e) mod n = ((a mod n)+(b mod n)+(c mod n)+(d mod n)+(e mod n)) mod n
  proof
    let a,b,c,d,e,n being Integer;
    thus (a+b+c+d+e) mod n = ((a+b+c+d) mod n + (e mod n)) mod n by NAT_D:66
    .= ((((a mod n)+(b mod n)+(c mod n)+(d mod n)) mod n) + ((e mod n) mod n))
    mod n by Th9
    .= ((a mod n)+(b mod n)+(c mod n)+(d mod n)+(e mod n)) mod n by NAT_D:66;
  end;
