
theorem Th2:
  for A being finite set st card A >= 3 holds for a,b being Element of A holds
  ex c being Element of A st c <> a & c <> b
proof
  let A9 be finite set;
  assume
A1: card A9 >= 3;
  then reconsider A = A9 as finite non empty set by CARD_1:27;
  let a,b be Element of A9;
 {a,b} c= A by ZFMISC_1:32;
then A2: card (A \ {a,b}) = card A - card {a,b} by CARD_2:44;
 card {a,b} <= 2 by CARD_2:50;
then  card (A \ {a,b}) >= 3 - 2 by A1,A2,XREAL_1:13;
then  card (A \ {a,b}) <> 0;
  then consider c being object such that
A3: c in A \ {a,b} by CARD_1:27,XBOOLE_0:def 1;
  reconsider c as Element of A9 by A3;
  take c;
 not c in {a,b} by A3,XBOOLE_0:def 5;
  hence thesis by TARSKI:def 2;
end;
