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 disjunctive implies H is conditional & H is negative &
  the_argument_of H is conjunctive & the_left_argument_of the_argument_of H is
  negative & the_right_argument_of the_argument_of H is negative
proof
  assume H is disjunctive;
  then
A1: H = (the_left_argument_of H) 'or' (the_right_argument_of H) by ZF_LANG:41;
  then H = 'not'(the_left_argument_of H) => (the_right_argument_of H);
  hence H is conditional & H is negative;
A2: the_argument_of H = 'not'(the_left_argument_of H) '&' 'not' (
  the_right_argument_of H) by A1,Th3;
  hence the_argument_of H is conjunctive;
  the_left_argument_of the_argument_of H = 'not'(the_left_argument_of H) &
the_right_argument_of the_argument_of H = 'not'(the_right_argument_of H) by A2
,Th4;
  hence thesis;
end;
