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 Th65:
  F is_subformula_of G & G is_subformula_of H implies F is_subformula_of H
proof
  assume that
A1: F is_subformula_of G and
A2: G is_subformula_of H;
  now
    assume F <> G;
    then
A3: F is_proper_subformula_of G by A1;
    now
      assume G <> H;
      then G is_proper_subformula_of H by A2;
      then F is_proper_subformula_of H by A3,Th64;
      hence thesis;
    end;
    hence thesis by A1;
  end;
  hence thesis by A2;
end;
