theorem
  [S,x] is quantifiable implies Sub_the_bound_of CQCSub_All([S,x],xSQ) = x
proof
  set S1 = CQCSub_All([S,x],xSQ);
  assume
A1: [S,x] is quantifiable;
  then S1 = Sub_All([S,x],xSQ) by Def5;
  then S1 is Sub_universal by A1,SUBSTUT1:14;
  then consider B being Element of [:QC-Sub-WFF(Al),bound_QC-variables(Al):],
   SQ being second_Q_comp of B such that
A2: S1 = Sub_All(B,SQ) and
A3: B`2 = Sub_the_bound_of S1 and
A4: B is quantifiable by SUBSTUT1:def 33;
  [S,x]`2 = B`2 by A1,A2,A4,Th36;
  hence thesis by A3;
end;
