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 'or' q
  is closed
proof
  let p,q be QC-formula of A;
A1: p 'or' q = 'not'('not' p '&' 'not' q) by QC_LANG2:def 3;
  'not' p '&' 'not' q is closed iff 'not' p is closed & 'not' q is closed
  by Th22;
  hence thesis by A1,Th21;
end;
