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
  All(x,'not' H) is_proper_subformula_of Ex(x,H) & 'not' H
  is_proper_subformula_of Ex(x,H)
proof
  All(x,'not' H) is_immediate_constituent_of Ex(x,H);
  hence
A1: All(x,'not' H) is_proper_subformula_of Ex(x,H) by ZF_LANG:61;
  'not' H is_immediate_constituent_of All(x,'not' H);
  hence thesis by A1,Th40;
end;
