<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</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">x</font>, <font color="Olive" title="b2">y</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a><br/> for <font color="Olive" title="b3">M</font> being 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>  holds <br/> ( <font color="Olive" title="b3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b3">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K14" title="ZF_LANG:func.14">All</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Maroon" title="c1">H</font> )</span><br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</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">M</font> being 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>  holds <br/> ( <font color="Olive" title="b1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b1">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K14" title="ZF_LANG:func.14">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> )</span><br/><b>let </b><font color="Maroon" title="c4">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"> ( <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K14" title="ZF_LANG:func.14">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> )</span><br/>







<a NAME="E1:89"/>
( ( <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K14" title="ZF_LANG:func.14">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> ) &amp; ( <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K14" title="ZF_LANG:func.14">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> implies <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> ) )
 
<b>by </b><i><a class="ref" href="zf_model.html#T25" title="ZF_MODEL:th.25">ZF_MODEL:25</a></i>;<br/>
<b>hence </b><a NAME="E2:89"/>
( <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c4">M</font> <a href="zf_model.html#R2" title="ZF_MODEL:pred.2">|=</a>  <a href="zf_lang.html#K14" title="ZF_LANG:func.14">All</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
