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<b>let </b><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">M</font>, <font color="Maroon" title="c3">N</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</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">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">N</font> implies <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> )</span><br/>





<b>assume </b><a NAME="E1:160"/><i><font color="Green" title="E80">A1</font></i>: 
( <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">N</font> &amp; not <font color="Maroon" title="c2">M</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">N</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:160"/><b>then </b>
( <font color="Maroon" title="c3">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c1">K</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">K</font> )
 
<b>by </b><i><a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</a></i>;<br/>
<a NAME="E3:160"/><b>then </b>
<font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c3">N</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c1">K</font> <a href="card_2.html#K2" title="CARD_2:func.2">*`</a> <font color="Maroon" title="c2">M</font>
 
<b>by </b><i><a class="ref" href="card_3.html#T136" target="_self" title="CARD_3:th.136">Th68</a></i>;<br/>
<b>hence </b><a NAME="E4:160"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:160"><i><font color="Green" title="E80">A1</font></i></a>, <a class="ref" href="card_1.html#T14" title="CARD_1:th.14">CARD_1:14</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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