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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <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"> for <font color="Olive" title="b1">F1</font>, <font color="Olive" title="b2">F2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="zf_lang.html#K9" title="ZF_LANG:func.9">WFF</a>   st <font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Olive" title="b1">F1</font> &amp; <font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Olive" title="b2">F2</font> holds <br/><font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Olive" title="b1">F1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">F2</font></span><br/><b>let </b><font color="Maroon" title="c2">F1</font>, <font color="Maroon" title="c3">F2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="zf_lang.html#K9" title="ZF_LANG:func.9">WFF</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">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Maroon" title="c2">F1</font> &amp; <font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Maroon" title="c3">F2</font> implies <font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Maroon" title="c2">F1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">F2</font> )</span><br/>





<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Maroon" title="c2">F1</font> &amp; <font color="Maroon" title="c1">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Maroon" title="c3">F2</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">M</font> <a href="zfrefle1.html#R1" title="ZFREFLE1:pred.1">|=</a> <font color="Maroon" title="c2">F1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">F2</font></span><br/>

<b>let </b><font color="Maroon" title="c4">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="zfrefle1.html#D1" target="_self" title="ZFREFLE1:def.1">ZFREFLE1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">F2</font> implies <font color="Maroon" title="c1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c4">H</font> )</span><br/>

<b>assume </b><a NAME="E2:7"/>
<font color="Maroon" title="c4">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c3">F2</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">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c4">H</font></span><br/>

<a NAME="E3:7"/><b>then </b>
( <font color="Maroon" title="c4">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F1</font> or <font color="Maroon" title="c4">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">F2</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:7"/>
<font color="Maroon" title="c1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="zfrefle1.html#D1" target="_self" title="ZFREFLE1:def.1">Def1</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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