reserve Al for QC-alphabet;
reserve a,b,b1 for object,
  i,j,k,n for Nat,
  p,q,r,s for Element of CQC-WFF(Al),
  x,y,y1 for bound_QC-variable of Al,
  P for QC-pred_symbol of k,Al,
  l,ll for CQC-variable_list of k,Al,
  Sub,Sub1 for CQC_Substitution of Al,
  S,S1,S2 for Element of CQC-Sub-WFF(Al),
  P1,P2 for Element of QC-pred_symbols(Al);

theorem Th12:
  for p, Sub holds ex S st S`1 = p & S`2 = Sub
proof
  defpred P[Element of CQC-WFF(Al)] means
      for Sub holds ex S st S`1 = $1 & S`2 = Sub;
A1: for p,q,x,k for ll being CQC-variable_list of k,Al for P being
QC-pred_symbol of k,Al holds P[VERUM(Al)] & P[P!ll] &
(P[p] implies P['not' p]) & (P[p] & P[q] implies P[p '&' q]) &
(P[p] implies P[All(x,p)]) by Th1,Th2,Th4,Th5,Th11;
  thus for p holds P[p] from CQC_LANG:sch 1(A1);
end;
