reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;
reserve sq,sq9 for FinSequence;

theorem Th43:
  H is existential implies (x = bound_in H iff ex H1 st Ex(x,H1) =
  H) & (H1 = the_scope_of H iff ex x st Ex(x,H1) = H)
proof
  assume
A1: H is existential;
  then ex y,F st H = Ex(y,F);
  then H.1 = 2 by FINSEQ_1:41;
  then not H is universal by Th22;
  hence thesis by A1,Def33,Def34;
end;
