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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c2">B</font> implies <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font> )</span><br/>



<b>assume </b><a NAME="E1:34"/><i><font color="Green" title="E23">A1</font></i>: 
 <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c2">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font></span><br/>

<div><i><font color="Green" title="E24">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</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="E2:34_1"/><b>then </b>
 <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="ref" href="card_1.html#T41" target="_self" title="CARD_1:th.41">Th41</a></i>;<br/><b>hence </b><a NAME="E3:34_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E23">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:34_2"/>
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</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="E2:34_2"/><b>then </b>
 <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="card_1.html#K3" title="CARD_1:func.3">alef</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="card_1.html#T41" target="_self" title="CARD_1:th.41">Th41</a></i>;<br/><b>hence </b><a NAME="E3:34_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:34"><i><font color="Green" title="E23">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:34"/>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="txt" href="#E2:34"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="ordinal1.html#T24" title="ORDINAL1:th.24">ORDINAL1:24</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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