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,y] in [:{x1},{y1}:] iff x = x1 & y = y1
proof
  x=x1 & y=y1 iff x in {x1} & y in {y1} by TARSKI:def 1;
  hence thesis by Lm16;
end;
