reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);

theorem Th13:
  Ex(x,p) = Ex(y,q) implies x = y & p = q
proof
  assume Ex(x,p) = Ex(y,q);
  then
A1: All(x,'not' p) = All(y,'not' q) by FINSEQ_1:33;
  then 'not' p = 'not' q by Th5;
  hence thesis by A1,Th5,FINSEQ_1:33;
end;
