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
  H is existential implies H is negative & the_argument_of H is
  universal & the_scope_of the_argument_of H is negative
proof
  assume H is existential;
  then
A1: H = Ex(bound_in H, the_scope_of H) by ZF_LANG:45;
  hence H is negative;
A2: the_argument_of H = All(bound_in H, 'not' the_scope_of H) by A1,Th3;
  hence the_argument_of H is universal;
  'not' the_scope_of H = the_scope_of the_argument_of H by A2,Th8;
  hence thesis;
end;
