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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:41"/>
( (  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> implies <font color="Maroon">X</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="wellord2.html#R2">are_equipotent</a>  ) &amp; ( <font color="Maroon">X</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="wellord2.html#R2">are_equipotent</a>  implies  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> ) &amp; ( <font color="Maroon">X</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="wellord2.html#R2">are_equipotent</a>  implies  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span> ) &amp; (  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span> implies <font color="Maroon">X</font>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="wellord2.html#R2">are_equipotent</a>  ) )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:41"/>
(  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> iff  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span> )
 ;<br/>


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