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

<b>assume </b><a NAME="E1:9"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">E</font> is <a href="ordinal1.html#V1">epsilon-transitive</a>
 ;<br/>

<b>hence </b><a NAME="E2:9"/>
( <font color="Maroon">E</font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K10">the_axiom_of_power_sets</a>  implies for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> holds <br/><font color="Maroon">E</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">X</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> )
 <b>by </b><i/>;<br/>

<b>assume </b><a NAME="E3:9"/>
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font> holds <br/><font color="Maroon">E</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">X</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font>
 ;<br/>

<a NAME="E4:9"/><b>then </b>
for <font color="Olive">u</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> holds  <font color="Maroon">E</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Olive">u</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font>
 
;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon">E</font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K10">the_axiom_of_power_sets</a> 
 <b>by </b><i>, </i>;<br/>


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