
theorem Th1:
  for A being finite set st card A >= 2 holds for a being Element of A holds
  ex b being Element of A st b <> a
proof
  let A9 be finite set;
  assume
A1: card A9 >= 2;
  then reconsider A = A9 as finite non empty set by CARD_1:27;
  let a be Element of A9;
 {a} c= A by ZFMISC_1:31;
then  card (A \ {a}) = card A - card {a} by CARD_2:44
    .= card A - 1 by CARD_1:30;
then  card (A \ {a}) <> 0 by A1;
  then consider b being object such that
A2: b in A \ {a} by CARD_1:27,XBOOLE_0:def 1;
  reconsider b as Element of A9 by A2;
  take b;
 not b in {a} by A2,XBOOLE_0:def 5;
  hence thesis by TARSKI:def 1;
end;
