reserve k,m,n for Element of NAT,
  a,X,Y for set,
  D,D1,D2 for non empty set;
reserve p,q for FinSequence of NAT;
reserve x,y,z,t for Variable;
reserve F,F1,G,G1,H,H1 for ZF-formula;

theorem Th23:
  H is being_equality & H.1 = 0 or H is being_membership & H.1 = 1
or H is negative & H.1 = 2 or H is conjunctive & H.1 = 3 or H is universal & H.
  1 = 4
proof
  per cases by Th9;
  case
    H is being_equality;
    hence thesis by Th18;
  end;
  case
    H is being_membership;
    hence thesis by Th19;
  end;
  case
    H is negative;
    hence thesis by Th20;
  end;
  case
    H is conjunctive;
    hence thesis by Th21;
  end;
  case
    H is universal;
    hence thesis by Th22;
  end;
end;
