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<b>let </b><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">v'</font>) where <font color="Olive" title="b1">v'</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">v'</font>] </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">v</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E3:1_1"/><i><font color="Green" title="E2">A2</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c2">v</font>)
 <b>and </b><br/><a NAME="E4:1_1"/><i><font color="Green" title="E3">A3</font></i>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c2">v</font>]
 ;<br/>
<a NAME="E5:1_1"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c2">v</font>]
 
<b>by </b><i><a class="txt" href="fraenkel.html#E1:1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="txt" href="fraenkel.html#E4:1_1"><i><font color="Green" title="E3">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">u'</font>) where <font color="Olive" title="b1">u'</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() : <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">u'</font>] </span>}</span> 
 <b>by </b><i><a class="txt" href="fraenkel.html#E3:1_1"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>


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