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

theorem
  X c= Y \ X implies X = {}
proof
  assume
A1: X c= Y \ X;
  thus X c= {}
  proof
    let x be object;
    assume
A2: x in X;
    then x in Y \ X by A1;
    hence thesis by A2,XBOOLE_0:def 5;
  end;
  thus thesis;
end;
