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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/>

<b>assume </b><a NAME="E1:6"/>
 <a href="ordinal1.html#K5">omega</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:6"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="ordinal1.html#V1">epsilon-transitive</a> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K7">the_axiom_of_pairs</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K8">the_axiom_of_unions</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K9">the_axiom_of_infinity</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K10">the_axiom_of_power_sets</a>  &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 1</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 2</span>)</span></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#R1">misses</a>  <a href="zf_model.html#K2">Free</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="zf_model.html#R2">|=</a>  <a href="zf_model.html#K11">the_axiom_of_substitution_for</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="zf_refle.html#T2" target="_self">Th2</a>, <a class="ref" href="zf_refle.html#T3" target="_self">Th3</a>, <a class="ref" href="zf_refle.html#T4" target="_self">Th4</a>, <a class="ref" href="zf_refle.html#T5" target="_self">Th5</a>, <a class="ref" href="zf_refle.html#T6" target="_self">Th6</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_model.html#D12">ZF_MODEL:def 12</a><br/>


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