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<b>let </b><font color="Maroon" title="c1">W</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">W</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_model.html#K7" title="ZF_MODEL:func.7">the_axiom_of_pairs</a> </span><br/>

<a NAME="E1:1"/>
( <font color="Maroon" title="c1">W</font> is <a href="ordinal1.html#V1" title="ORDINAL1:attr.1">epsilon-transitive</a> &amp; ( for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">W</font> holds  <span class="p1"><a href="classes2.html#K5" title="CLASSES2:func.5">{</a><span class="default"><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font></span><a href="classes2.html#K5" title="CLASSES2:func.5">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">W</font> ) )
 
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<b>hence </b><a NAME="E2:1"/>
<font color="Maroon" title="c1">W</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_model.html#K7" title="ZF_MODEL:func.7">the_axiom_of_pairs</a> 
 <b>by </b><i><a class="ref" href="zfmodel1.html#T2" title="ZFMODEL1:th.2">ZFMODEL1:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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