&gt; 
&gt; 1) The &lt;=&gt; axiom above is invalid and probably could be used to
&gt; prove a contradiction.
&gt; 
&gt; 2) An augmented &lt;=&gt; axiom like the one above but disallowing 
&gt; two receivers, etc., might not lead to contradictions and
&gt; a generalization of it might be OK in the SUO.  
&gt; 
&gt; 3) I certainly would not personally want to 
&gt; call the change from what precedes the &lt;=&gt; to
&gt; what follows the &lt;=&gt; a "reduction". 

MW: Indeed, the only thing that is reduced is