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<b>take </b>
1
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not 1 is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; 1 is <a href="membered.html#V6" title="MEMBERED:attr.6">natural-membered</a> )</span><br/>

<b>thus </b><a NAME="E1:3_1_1"/>
not 1 is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 1 is <a href="membered.html#V6" title="MEMBERED:attr.6">natural-membered</a></span><br/>

<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D6" target="_self" title="MEMBERED:def.6">MEMBERED:def 6</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1 implies <font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> )</span><br/>

<b>assume </b><a NAME="E2:3_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a></span><br/>

<b>hence </b><a NAME="E3:3_1_1"/>
<font color="Maroon" title="c1">x</font> is <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>
 <b>by </b><i><a class="ref" href="card_1.html#T87" title="CARD_1:th.87">CARD_1:87</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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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