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
  (H is_immediate_constituent_of G or H is_proper_subformula_of G or H
  is_subformula_of G) & G in Subformulae F implies H in Subformulae F
proof
  assume that
A1: H is_immediate_constituent_of G or H is_proper_subformula_of G or H
  is_subformula_of G and
A2: G in Subformulae F;
  H is_proper_subformula_of G or H is_subformula_of G by A1,Th61;
  then
A3: H is_subformula_of G;
  G is_subformula_of F by A2,Th78;
  then H is_subformula_of F by A3,Th65;
  hence thesis by Def42;
end;
