<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/>









<b>assume </b><a NAME="E1:164"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:164"/>
( (  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">z</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <font color="Maroon">z</font>,<font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> implies  <a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> ) &amp; (  <a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> implies  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">z</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <font color="Maroon">z</font>,<font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> ) &amp; (  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> implies  <a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> ) &amp; (  <a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">z</font>,<span class="p2">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> implies  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> ) &amp; (  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> implies <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> ) &amp; ( <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> implies  <a href="zf_lang.html#K6">'not'</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6">'not'</a> <font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> ) )
 
<b>by </b><i>, <a class="ref" href="zf_lang1.html#T66" target="_self">Th66</a>, <a class="ref" href="zf_lang1.html#T74" target="_self">Th74</a></i>;<br/>
<b>hence </b><a NAME="E3:164"/>
(  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">z</font>,<font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <font color="Maroon">z</font>,<font color="Maroon">H</font></span>)</span> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> iff <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> )
 ;<br/>


</div>
