theorem
  H is conditional implies the_antecedent_of H = the_left_argument_of
  the_argument_of H
proof
  assume H is conditional;
  then H = (the_antecedent_of H) => (the_consequent_of H) by ZF_LANG:47;
  then
  the_argument_of H = (the_antecedent_of H) '&' 'not'(the_consequent_of H)
  by Th3;
  hence thesis by Th4;
end;
