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<a NAME="E1:3_1_1"/>
 <a href="unialg_2.html#K9">Sub</a> <font color="Maroon">c<sub>1</sub></font> is    <a href="unialg_3.html#M1" target="_self">SubAlgebra-Family</a> of <font color="Maroon">c<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_3.html#D1" target="_self">UNIALG_3:def 1</a><br/>

<b>assume </b><a NAME="E1:3_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="unialg_2.html#K9">Sub</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:3_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is    <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="unialg_2.html#D15">UNIALG_2:def 15</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:3_1_1"/>
 <a href="unialg_2.html#K9">Sub</a> <font color="Maroon">c<sub>1</sub></font> is  non <a href="xboole_0.html#V1">empty</a>  <a href="unialg_3.html#M1" target="_self">SubAlgebra-Family</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>


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