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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="cat_1.html#M2" target="_self">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</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>6</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>









<b>assume </b><a NAME="E1:107"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:107"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T116">FUNCT_2:116</a></i>;<br/>
<b>hence </b><a NAME="E3:107"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T123" target="_self">Th123</a></i>;<br/>


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