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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">b</font> &amp; <font color="Maroon" title="c2">b</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">c</font> implies <font color="Maroon" title="c1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">c</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green" title="E3">A1</font></i>: 
<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>
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c2">b</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c3">c</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> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">c</font></span><br/>

<a NAME="E3:3"/>
<font color="Maroon" title="c2">b</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="subset.html#E2:3"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="subset.html#T3" target="_self" title="SUBSET:th.3">Th3</a></i>;<br/>
<a NAME="E4:3"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="subset.html#E1:3"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:3"/>
<font color="Maroon" title="c1">a</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="ref" href="subset.html#T1" target="_self" title="SUBSET:th.1">Th1</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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