theorem
  ex i st (A)a.i = a
proof
  consider x,y being object such that
A1: x in {6} and
A2: y in NAT and
A3: [x,y] = a by ZFMISC_1:def 2;
  reconsider i = y as Nat by A2;
  take i;
  thus thesis by A1,A3,TARSKI:def 1;
end;
