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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/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:67"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T19">CAT_1:19</a></i>;<br/>
<a NAME="E2:67"/><b>then </b>
( (  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T52">CAT_1:52</a></i>;<br/>
<b>hence </b><a NAME="E3:67"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span><a href="domain_1.html#K1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K18" target="_self">hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K1">]</a></span> is    <a href="subset_1.html#M1">Element</a> of  <a href="ens_1.html#K2" target="_self">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="ens_1.html#T5" target="_self">Th5</a></i>;<br/>


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