reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;
reserve F,G,H,H1 for Element of QC-WFF(A);
reserve x,y,z for bound_QC-variable of A,
  k,n,m for Nat,
  P for ( QC-pred_symbol of k, A),
  V for QC-variable_list of k, A;
reserve L,L9 for FinSequence;

theorem Th83:
  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 be Element of QC-WFF(A) such that
A2: F1 = a and
A3: F1 is_subformula_of F by Def22;
  F1 is_subformula_of H by A1,A3,Th57;
  hence thesis by A2,Def22;
end;
