reserve A for QC-alphabet;
reserve i,j,k for Nat;
reserve f for Substitution of A;
reserve x,y for bound_QC-variable of A;
reserve a for free_QC-variable of A;
reserve p,q for Element of QC-WFF(A);
reserve l,l1,l2,ll for FinSequence of QC-variables(A);
reserve r,s for Element of CQC-WFF(A);

theorem Th17:
  for k being Nat
  for P being QC-pred_symbol of k,A for l being QC-variable_list of
  k,A holds (P!l).x = P!Subst(l,(A)a.0.-->x)
proof let k be Nat;
  let P be QC-pred_symbol of k,A;
  let l be QC-variable_list of k, A;
  reconsider P9 = P as QC-pred_symbol of A;
A1: P!l is atomic by QC_LANG1:def 18;
  then the_arguments_of (P!l) = l & the_pred_symbol_of (P!l) = P9 by
QC_LANG1:def 22,def 23;
  hence thesis by A1,Th16;
end;
