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 Th12:
  for p being QC-formula of A holds still_not-bound_in All(x,p) = (
  still_not-bound_in p) \ {x}
proof
  let p be QC-formula of A;
  set a = All(x,p);
A1: a is universal;
  then the_scope_of a = p & bound_in a = x by QC_LANG1:def 27,def 28;
  hence thesis by A1,Th11;
end;
