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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:14"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="zf_model.html#NR3" target="_self">is_a_model_of_ZF</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="zfrefle1.html#R2" target="_self">&lt;==&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:14"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="zfrefle1.html#R1" target="_self">|=</a>  <a href="zfrefle1.html#K2" target="_self">ZF-axioms</a> 
 
<b>by </b><i><a class="ref" href="zfrefle1.html#T4" target="_self">Th4</a></i>;<br/>
<a NAME="E3:14"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="zfrefle1.html#R1" target="_self">|=</a>  <a href="zfrefle1.html#K2" target="_self">ZF-axioms</a> 
 
<b>by </b><i><a class="txt" href="zfrefle1.html#E1:14"><i><font color="Green">E10</font></i></a>, <a class="ref" href="zfrefle1.html#T8" target="_self">Th8</a></i>;<br/>
<b>hence </b><a NAME="E4:14"/>
(  not <font color="Maroon">c<sub>2</sub></font> is <a href="ordinal1.html#V1">epsilon-transitive</a> or <font color="Maroon">c<sub>2</sub></font> <a href="zf_model.html#NR3" target="_self">is_a_model_of_ZF</a>  )
 <b>by </b><i><a class="ref" href="zfrefle1.html#T5" target="_self">Th5</a></i>;<br/>


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