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;
reserve sq,sq9 for FinSequence;
reserve L,L9 for FinSequence;
reserve j,j1 for Element of NAT;

theorem
  H is atomic implies not F is_proper_subformula_of H
proof
  assume H is atomic;
  then H is being_equality or H is being_membership;
  then H = (Var1 H) '=' Var2 H or H = (Var1 H) 'in' Var2 H by Th36,Th37;
  hence thesis by Th67,Th68;
end;
