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
  F is_subformula_of H implies Subformulae F c= Subformulae H
proof
  assume
A1: F is_subformula_of H;
  let a be object;
  assume a in Subformulae F;
  then consider F1 such that
A2: F1 = a and
A3: F1 is_subformula_of F by Def42;
  F1 is_subformula_of H by A1,A3,Th65;
  hence thesis by A2,Def42;
end;
