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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Olive" title="b1">f</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c2">f</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:33"/>
<font color="Maroon" title="c2">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">f</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> </span><br/>

<a NAME="E2:33"/><span class="kw">then </span>
<font color="Maroon" title="c2">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font>
 
;<br/>
<a NAME="E3:33"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">g</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Olive" title="b1">g</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:33"/>
<font color="Maroon" title="c2">f</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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