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<span class="kw">consider </span><font color="Maroon" title="c1">b</font> being   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><br/><a NAME="E2:134"/><span class="lab"><font color="Green" title="E73">A0</font></span>: 
1 <a href="ordinal6.html#K13" title="ORDINAL6:func.13">-Veblen</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c1">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal6.html#T75" target="_self" title="ORDINAL6:th.75">Th13</a>, <a class="ref" href="ordinal5.html#T51" title="ORDINAL5:th.51">ORDINAL5:51</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">a</font> being   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <span class="kw"> such that </span><br/><a NAME="E4:134"/><span class="lab"><font color="Green" title="E74">A1</font></span>: 
 <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="ordinal6.html#K13" title="ORDINAL6:func.13">-Veblen</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal6.html#T76" target="_self" title="ORDINAL6:th.76">Th14</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="134_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:134_1"/>
<font color="Maroon" title="c1">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:134_1"/><span class="kw">then </span>
 <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c1">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal3.html#T8" title="ORDINAL3:th.8">ORDINAL3:8</a>, <a class="ref" href="ordinal5.html#T44" title="ORDINAL5:th.44">ORDINAL5:44</a></span>;<br/><span class="kw">hence </span><a NAME="E3:134_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:134"><span class="lab"><font color="Green" title="E73">A0</font></span></a>, <a class="txt" href="#E4:134"><span class="lab"><font color="Green" title="E74">A1</font></span></a>, <a class="ref" href="ordinal6.html#T72" target="_self" title="ORDINAL6:th.72">Th15a</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:134"/>
1 <a href="ordinal6.html#K13" title="ORDINAL6:func.13">-Veblen</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:134"><span class="lab"><font color="Green" title="E73">A0</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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