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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/>

<a NAME="E1:100"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="cat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="partfun1.html#K6">id</a> the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T52">FUNCT_1:52</a>, <a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<b>hence </b><a NAME="E2:100"/>
(  <a href="cat_1.html#K15" target="_self">id</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="cat_1.html#K15" target="_self">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12" target="_self">Obj</a> <span class="p2">(<span class="default"><a href="cat_1.html#K15" target="_self">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1" target="_self">Objects</a> of <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T117" target="_self">Th117</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D22" target="_self">CAT_1:def 22</a><br/>


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