reserve A for QC-alphabet;
reserve a,b,b1,b2,c,d for object,
  i,j,k,n for Nat,
  x,y,x1,x2 for bound_QC-variable of A,
  P for QC-pred_symbol of k,A,
  ll for CQC-variable_list of k,A,
  l1 ,l2 for FinSequence of QC-variables(A),
  p for QC-formula of A,
  s,t for QC-symbol of A;
reserve Sub for CQC_Substitution of A;
reserve finSub for finite CQC_Substitution of A;
reserve e for Element of vSUB(A);
reserve S,S9,S1,S2,S19,S29,T1,T2 for Element of QC-Sub-WFF(A);
reserve B for Element of [:QC-Sub-WFF(A),bound_QC-variables(A):];
reserve SQ for second_Q_comp of B;

theorem
  for B1,B2 being Element of [:QC-Sub-WFF(A),bound_QC-variables(A):], SQ1
being second_Q_comp of B1, SQ2 being second_Q_comp of B2 st B1 is quantifiable
  & B2 is quantifiable & Sub_All(B1,SQ1) = Sub_All(B2,SQ2) holds B1 = B2
proof
  let B1,B2 be Element of [:QC-Sub-WFF(A),bound_QC-variables(A):], SQ1 being
  second_Q_comp of B1, SQ2 being second_Q_comp of B2 such that
A1: B1 is quantifiable and
A2: B2 is quantifiable and
A3: Sub_All(B1,SQ1) = Sub_All(B2,SQ2);
A4: Sub_All(B1,SQ1) = [All(B1`2,(B1`1)`1),SQ1] & Sub_All(B2,SQ2) = [All(B2`2
  ,(B2 `1)`1),SQ2] by A1,A2,Def24;
  then All(B1`2,(B1`1)`1) = All(B2`2,(B2`1)`1) by A3,XTUPLE_0:1;
  then
A5: B1`2 = B2`2 & (B1`1)`1 = (B2`1)`1 by QC_LANG2:5;
  ex a,b being object
st a in QC-Sub-WFF(A) & b in bound_QC-variables(A) & B2 = [a,b] by
ZFMISC_1:def 2;
  then
A6: B2 = [B2`1,B2`2];
  ex a,b being object
st a in QC-Sub-WFF(A) & b in bound_QC-variables(A) & B1 = [a,b] by
ZFMISC_1:def 2;
  then
A7: B1 = [B1`1,B1`2];
A8: B1`1 = [(B1`1)`1,(B1`1)`2] & B2`1 = [(B2`1)`1,(B2`1)`2] by Th10;
  (B1`1)`2 = (QSub(A)).[All(B1`2,(B1`1)`1),SQ1] by A1,Def23;
  hence thesis by A2,A3,A4,A5,A8,A7,A6,Def23;
end;
