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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="oppcat_1.html#K2" target="_self">opp</a> </span>)</span>, <font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="oppcat_1.html#K2" target="_self">opp</a> </span>)</span>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>





<b>assume </b><a NAME="E1:11"/>
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:11"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="cat_1.html#D7">CAT_1:def 7</a></i>;<br/>
<a NAME="E3:11"/><b>then </b>
 <a href="oppcat_1.html#K6" target="_self">opp</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="oppcat_1.html#K4" target="_self">opp</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><a href="oppcat_1.html#K4" target="_self">opp</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:11"/>
 <a href="oppcat_1.html#K6" target="_self">opp</a> <font color="Maroon">f</font> is    <a href="cat_1.html#M1">Morphism</a> of  <a href="oppcat_1.html#K4" target="_self">opp</a> <font color="Maroon">b</font>, <a href="oppcat_1.html#K4" target="_self">opp</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="cat_1.html#D7">CAT_1:def 7</a></i>;<br/>


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