reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;

theorem
  'not' F is_subformula_of H implies F is_proper_subformula_of H
proof
  F is_immediate_constituent_of 'not' F;
  hence thesis by Th40;
end;
