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<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">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="E1:181"/>
<font color="Maroon">H</font> is <a href="zf_lang.html#V11">existential</a>
 ;<br/>

<a NAME="E2:181"/><b>then </b>
( <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> is <a href="zf_lang.html#V11">existential</a> &amp; <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K23">bound_in</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K24">the_scope_of</a> <font color="Maroon">H</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="zf_lang.html#T63">ZF_LANG:63</a></i>;<br/>
<a NAME="E3:181"/><b>then </b>
( <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K23">bound_in</a> <span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K24">the_scope_of</a> <span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span></span>)</span> &amp; (  <a href="zf_lang.html#K23">bound_in</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K13">Ex</a> <font color="Maroon">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K24">the_scope_of</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></span>)</span> ) &amp; (  <a href="zf_lang.html#K23">bound_in</a> <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> implies <font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K23">bound_in</a> <font color="Maroon">H</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K24">the_scope_of</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></span>)</span> ) )
 
<b>by </b><i>, , <a class="ref" href="zf_lang.html#T63">ZF_LANG:63</a></i>;<br/>
<b>hence </b><a NAME="E4:181"/>
(  <a href="zf_lang.html#K24">the_scope_of</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K24">the_scope_of</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#K23">bound_in</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies  <a href="zf_lang.html#K23">bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) &amp; (  <a href="zf_lang.html#K23">bound_in</a> <font color="Maroon">H</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x</font> implies  <a href="zf_lang.html#K23">bound_in</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">y</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="zf_lang.html#K23">bound_in</a> <font color="Maroon">H</font> ) )
 <b>by </b><i><a class="ref" href="zf_lang.html#T51">ZF_LANG:51</a></i>;<br/>


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