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<b>let </b><font color="Maroon" title="c1">E1</font>, <font color="Maroon" title="c2">E2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">E1</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> &amp; ( for <font color="Olive" title="b1">E</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">E</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> holds <br/><font color="Maroon" title="c1">E1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> ) &amp; <font color="Maroon" title="c2">E2</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> &amp; ( for <font color="Olive" title="b1">E</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">E</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> holds <br/><font color="Maroon" title="c2">E2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> ) implies <font color="Maroon" title="c1">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">E2</font> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:10_1_2"/><i><font color="Green" title="E9">A28</font></i>: 
( <font color="Maroon" title="c1">E1</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> &amp; ( for <font color="Olive" title="b1">E</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">E</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> holds <br/><font color="Maroon" title="c1">E1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> ) )
 <b>and </b><br/><a NAME="E2:10_1_2"/><i><font color="Green" title="E10">A29</font></i>: 
( <font color="Maroon" title="c2">E2</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> &amp; ( for <font color="Olive" title="b1">E</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">E</font> is <a href="intpro_1.html#V7" title="INTPRO_1:attr.7">MC-closed</a> holds <br/><font color="Maroon" title="c2">E2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">E</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">E2</font></span><br/>

<a NAME="E3:10_1_2"/>
( <font color="Maroon" title="c1">E1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">E2</font> &amp; <font color="Maroon" title="c2">E2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">E1</font> )
 
<b>by </b><i><a class="txt" href="intpro_1.html#E1:10_1_2"><i><font color="Green" title="E9">A28</font></i></a>, <a class="txt" href="intpro_1.html#E2:10_1_2"><i><font color="Green" title="E10">A29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:10_1_2"/>
<font color="Maroon" title="c1">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">E2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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