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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="hilbert1.html#K1" target="_self">HP-WFF</a> ;<br/>

<b>assume </b><a NAME="E1:33"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="hilbert1.html#V6" target="_self">Hilbert_theory</a>
 ;<br/>

<a NAME="E2:33"/>
 <a href="subset_1.html#K1">{}</a> <a href="hilbert1.html#K1" target="_self">HP-WFF</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E3:33"/><b>then </b>
 <a href="hilbert1.html#K6" target="_self">HP_TAUT</a>  <a href="tarski.html#R1">c=</a>  <a href="hilbert1.html#K5" target="_self">CnPos</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="hilbert1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E4:33"/>
 <a href="hilbert1.html#K6" target="_self">HP_TAUT</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="hilbert1.html#E1:33"><i><font color="Green">E23</font></i></a>, <a class="ref" href="hilbert1.html#T12" target="_self">Th12</a></i>;<br/>


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