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
  Free Ex(x,p) = Free p
proof
  Ex(x,p) = 'not' All(x,'not' p) by QC_LANG2:def 5;
  hence Free Ex(x,p) = Free All(x,'not' p) by Th39
    .= Free 'not' p by Th44
    .= Free p by Th39;
end;
