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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="card_4.html#V1" title="CARD_4:attr.1">countable</a> <a href="card_5.html#NM1" title="CARD_5:NM.1">Aleph</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">M</font> is <a href="card_fil.html#V6" title="CARD_FIL:attr.6">strongly_inaccessible</a> implies  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c1">M</font> is <a href="zf_model.html#V1" title="ZF_MODEL:attr.1">being_a_model_of_ZF</a> )</span><br/>

<b>assume </b><a NAME="E1:56"/>
<font color="Maroon" title="c1">M</font> is <a href="card_fil.html#V6" title="CARD_FIL:attr.6">strongly_inaccessible</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c1">M</font> is <a href="zf_model.html#V1" title="ZF_MODEL:attr.1">being_a_model_of_ZF</a></span><br/>

<a NAME="E2:56"/><b>then </b><i><font color="Green" title="E42">A1</font></i>: 
 <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c1">M</font> is   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>
 
<b>by </b><i><a class="ref" href="card_lar.html#T39" target="_self" title="CARD_LAR:th.39">Th39</a></i>;<br/>
<a NAME="E3:56"/>
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="card_4.html#T8" title="CARD_4:th.8">CARD_4:8</a></i>;<br/>
<a NAME="E4:56"/><b>then </b>
 <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a> <font color="Maroon" title="c1">M</font>
 
<b>by </b><i><a class="ref" href="card_4.html#T44" title="CARD_4:th.44">CARD_4:44</a>, <a class="ref" href="xboole_0.html#D8" title="XBOOLE_0:def.8">XBOOLE_0:def 8</a></i>;<br/>
<a NAME="E5:56"/><b>then </b>
(  <a href="ordinal1.html#K5" title="ORDINAL1:func.5">omega</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">M</font> &amp; <font color="Maroon" title="c1">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c1">M</font> )
 
<b>by </b><i><a class="ref" href="classes1.html#T44" title="CLASSES1:th.44">CLASSES1:44</a>, <a class="ref" href="ordinal1.html#T21" title="ORDINAL1:th.21">ORDINAL1:21</a></i>;<br/>
<b>hence </b><a NAME="E6:56"/>
 <a href="classes1.html#K4" title="CLASSES1:func.4">Rank</a> <font color="Maroon" title="c1">M</font> is <a href="zf_model.html#V1" title="ZF_MODEL:attr.1">being_a_model_of_ZF</a>
 <b>by </b><i><a class="txt" href="card_lar.html#E2:56"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="zf_refle.html#T7" title="ZF_REFLE:th.7">ZF_REFLE:7</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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