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 Th11:
  S is Sub_atomic implies S`1 is atomic
proof
  assume S is Sub_atomic;
  then consider
  k being Nat, P being (QC-pred_symbol of k,A), ll being
  QC-variable_list of k,A, e being Element of vSUB(A) such that
A1: S = Sub_P(P,ll,e);
  S = [P!ll,e] by A1,Th9;
  then S`1 = P!ll;
  hence thesis;
end;
