reserve i,k for Nat;
reserve A for QC-alphabet;
reserve x for bound_QC-variable of A;
reserve a for free_QC-variable of A;
reserve p,q for Element of QC-WFF(A);
reserve l for FinSequence of QC-variables(A);
reserve P,Q for QC-pred_symbol of A;
reserve V for non empty Subset of QC-variables(A);
reserve s,t for QC-symbol of A;

theorem Th19:
  for p being QC-formula of A holds still_not-bound_in Ex(x,p) = (
  still_not-bound_in p) \ {x}
proof
  let p be QC-formula of A;
  Ex(x,p) = 'not' All(x,'not' p) by QC_LANG2:def 5;
  hence still_not-bound_in Ex(x,p) = still_not-bound_in All(x,'not' p) by Th7
    .= (still_not-bound_in 'not' p) \ {x} by Th12
    .= (still_not-bound_in p) \ {x} by Th7;
end;
