theorem
  H is conditional implies (M,v |= H iff (M,v |= the_antecedent_of H
  implies M,v |= the_consequent_of H))
proof
  assume H is conditional;
  then H = (the_antecedent_of H) => (the_consequent_of H) by ZF_LANG:47;
  hence thesis by ZF_MODEL:18;
end;
