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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">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>



<b>thus </b><a NAME="E1:72"/>
( <font color="Maroon">b</font> is <a href="cat_1.html#V6" target="_self">terminal</a> implies for <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>  ex <font color="Olive">f</font> being   <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Olive">a</font>,<font color="Maroon">b</font> st  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Olive">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">f</font></span><a href="tarski.html#K1">}</a></span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:72_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">b</font> is <a href="cat_1.html#V6" target="_self">terminal</a>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>

<b>consider </b><font color="Maroon">f</font> being    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font><b> such that </b><br/><a NAME="E3:72_1"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">g</font> being   <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font> holds  <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font>
 <b>by </b><i>, </i>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<a NAME="E4:72_1"/>
 <a href="cat_1.html#K6" target="_self">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> 
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E5:72_1"/>
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:72"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">a</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>  ex <font color="Olive">f</font> being   <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Olive">a</font>,<font color="Maroon">b</font> st  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Olive">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">f</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D15" target="_self">CAT_1:def 15</a><br/>

<b>consider </b><font color="Maroon">f</font> being    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font><b> such that </b><br/><a NAME="E4:72"/><i><font color="Green">E23</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">f</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E5:72"/>
 <a href="cat_1.html#K6" target="_self">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> 
 <b>by </b><i/>;<br/>

<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E6:72"/>
for <font color="Olive">g</font> being   <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font> holds  <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font>
 <b>by </b><i>, </i>;<br/>


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