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 Th19:
  [p '&' q,Sub] = CQCSub_&([p,Sub],[q,Sub])
proof
  set S1 = [p,Sub];
  set S2 = [q,Sub];
A1: S1`1 = p & S2`1 = q;
A2: S1`2 = Sub & S2`2 = Sub;
  then CQCSub_&(S1,S2) = Sub_&(S1,S2) by SUBLEMMA:def 3;
  hence thesis by A2,A1,SUBSTUT1:def 21;
end;
