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

theorem
  X \ Y c= Z implies X c= Y \/ Z
proof
  assume
A1: for x being object holds x in X \ Y implies x in Z;
  let x be object;
  assume x in X;
  then x in X \ Y or x in Y by XBOOLE_0:def 5;
  then x in Z or x in Y by A1;
  hence thesis by XBOOLE_0:def 3;
end;
