
theorem
  for A being 2-element set holds
    ex a, b being Element of A st a <> b & A = {a, b}
  proof
    let A be 2-element set;
    card A = 2 by CARD_1:def 7; then
    consider c, d being object such that
A1: c <> d & A = {c, d} by CARD_2:60;
    c in A & d in A by A1,TARSKI:def 2;
    hence thesis by A1;
  end;
