reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

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;
