  From here the argument for simple conditioning is a matter of using (3.4) and (3.5) to establish ordinal similarity.  Suppose that H and H* entail E and that P(H) &gt; P(H*).  It follows from (3.5) that LR(H, H*; E) = 1 and LR(~H, ~H*; ~E) &gt; 1. (3.4) then entails that any learning experience that raises E's probability must result in a posterior with Q(H) &gt; Q(H*).  Thus, Q and P are ordinally similar with respect to hypotheses that entail H.  If we go on to suppose that the learning experience raises E's probability to 1, then (3.6) then guarantees that Q arises from P by simple conditioning on E.