reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem
  X \ Y = Y \ X implies X = Y
proof
  assume
A1: X \ Y = Y \ X;
  now
    let x be object;
    x in X & not x in Y iff x in Y \ X by A1,XBOOLE_0:def 5;
    hence x in X iff x in Y by XBOOLE_0:def 5;
  end;
  hence thesis by TARSKI:2;
end;
