theorem Th38:
  CQC_Sub(S) is Element of CQC-WFF(A) & [S,x] is quantifiable implies
  CQC_Sub(Sub_All([S,x],xSQ)) is Element of CQC-WFF(A)
proof
  set S9 = Sub_All([S,x],xSQ);
  assume that
A1: CQC_Sub(S) is Element of CQC-WFF(A) and
A2: [S,x] is quantifiable;
  Sub_the_scope_of S9 = [S,x]`1 by A2,Th21;
  then
  Quant(S9,CQC_Sub(Sub_the_scope_of S9)) = All(S_Bound(@S9),CQC_Sub(S));
  then Quant(S9,CQC_Sub(Sub_the_scope_of S9)) is Element of CQC-WFF(A) by A1,
CQC_LANG:13;
  hence thesis by A2,Th14,Th32;
end;
