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;
