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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:40_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="frechet.html#R1">is_convergent_to</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:40_1_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="frechet.html#R1">is_convergent_to</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:40_1_2"/><i><font color="Green">E36</font></i>: 
 <a href="frechet.html#K1">Lim</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="frechet2.html#E1:40"><i><font color="Green">E33</font></i></a></i>;<br/>
<a NAME="E5:40_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="frechet.html#K1">Lim</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="frechet2.html#E1:40_1_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="frechet.html#D4">FRECHET:def 4</a></i>;<br/>
<a NAME="E6:40_1_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="frechet2.html#E4:40_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E7:40_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="frechet2.html#E2:40_1_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="frechet2.html#E4:40_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="frechet.html#D4">FRECHET:def 4</a></i>;<br/>
<b>hence </b><a NAME="E8:40_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="frechet2.html#E6:40_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


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