
theorem NE:
  for X be set, S be non empty diff-closed Subset-Family of X holds
    {} in S
proof
   let X be set, S be non empty diff-closed Subset-Family of X;
   consider A be object such that
A1: A in S by XBOOLE_0:def 1;
   reconsider A as set by TARSKI:1;
   A \ A in S by A1,FINSUB_1:def 3;
   hence {} in S by XBOOLE_1:37;
end;
