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;
reserve L,L9 for FinSequence;
reserve j,j1 for Element of NAT;

theorem
  G is_subformula_of H & H is_subformula_of G implies G = H
proof
  assume that
A1: G is_subformula_of H and
A2: H is_subformula_of G;
  assume
A3: G <> H;
  then G is_proper_subformula_of H by A1;
  then
A4: len G < len H by Th62;
  H is_proper_subformula_of G by A2,A3;
  hence contradiction by A4,Th62;
end;
