reserve X for set;
reserve UN for Universe;

theorem
  X is axiom_GU2
  implies
  (for x being set st x in X holds {x} in X)
  proof
    assume
A1: X is axiom_GU2;
    let x be set;
    assume
A2: x in X;
    {x} = {x,x} by ENUMSET1:29;
    hence {x} in X by A1,A2;
  end;
