reserve x,y,z,X,Y for set;
reserve X,Y for non empty set,
  f for Function of X,Y;
reserve X, Y for non empty set,
  F for (BinOp of Y),
  B for (Element of Fin X),
  f for Function of X,Y;
reserve A for set,
  x,y,z for Element of Fin A;
reserve X,Y for non empty set,
  A for set,
  f for (Function of X, Fin A),
  i,j,k for (Element of X);

theorem Th52:
  for x being set, y being Element of X holds x in singleton X.y iff x = y
proof
  let x be set, y be Element of X;
  singleton X.y = {y} by Th51;
  hence thesis by TARSKI:def 1;
end;
