reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;
reserve M for non empty set,
  m,m9 for Element of M,
  v,v9 for Function of VAR,M;
reserve i,j for Element of NAT;

theorem
  ex i st x = x.i
proof
  x in VAR;
  then consider j such that
A1: x = j and
A2: 5 <= j;
  consider i be Nat such that
A3: j = 5+i by A2,NAT_1:10;
  reconsider i as Element of NAT by ORDINAL1:def 12;
  take i;
  thus thesis by A1,A3;
end;
