theorem
  x in X & (not y in X or x = y) implies {x,y} /\ X = {x}
proof
  assume
A1: x in X &( not y in X or x=y);
  for z holds z in {x,y} /\ X iff z=x
  proof
    let z be object;
    z in {x,y} /\ X iff z in {x,y} & z in X by XBOOLE_0:def 4;
    hence thesis by A1,TARSKI:def 2;
  end;
  hence thesis by TARSKI:def 1;
end;
