
theorem Lemma3:
  for A being 2-element set, a, b being Element of A st
    a <> b holds A = {a, b}
  proof
    let A be 2-element set, a, b be Element of A;
    assume
A0: a <> b;
    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;
    a = c or a = d by TARSKI:def 2,A1;
    hence thesis by A0,TARSKI:def 2,A1;
  end;
