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
  for p,q being QC-formula of A holds p is closed & q is closed iff p <=> q
  is closed
proof
  let p,q be QC-formula of A;
  p <=> q = (p => q) '&' (q => p) by QC_LANG2:def 4;
  then p <=> q is closed iff p => q is closed & q => p is closed by Th22;
  hence thesis by Th26;
end;
