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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:7"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">c<sub>1</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="unialg_3.html#K1" target="_self">Sub</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:7_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is  <a href="unialg_1.html#V3">strict</a>  <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/>
<b>hence </b><a NAME="E3:7_1"/>
ex <font color="Olive">b<sub>1</sub></font> being <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>


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

<b>thus </b><a NAME="E2:7"/>
( ex <font color="Olive">b<sub>1</sub></font> being <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3">SubAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="unialg_3.html#K1" target="_self">Sub</a> <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/>


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