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<b>thus </b><a NAME="E1:21_1_1"/>
( <font color="Maroon" title="c1">X</font> is <a href="cat_5.html#V2" title="CAT_5:attr.2">categorial</a> implies for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">x</font> is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> )
 <b>by </b><i><a class="ref" href="cat_5.html#D4" target="_self" title="CAT_5:def.4">Def4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">x</font> is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> ) implies <font color="Maroon" title="c1">X</font> is <a href="cat_5.html#V2" title="CAT_5:attr.2">categorial</a> )</span><br/>

<b>assume </b><a NAME="E2:21_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">x</font> is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</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> is <a href="cat_5.html#V2" title="CAT_5:attr.2">categorial</a></span><br/>

<b>let </b><font color="Maroon" title="c2">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="cat_5.html#D4" target="_self" title="CAT_5:def.4">CAT_5:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c2">x</font> is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> )</span><br/>

<b>thus </b><a NAME="E3:21_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c2">x</font> is   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> )
 <b>by </b><i><a class="txt" href="cat_5.html#E2:21_1_1"><i><font color="Green" title="E13">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/>


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