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

<b>let </b><font color="Maroon" title="c1">Y</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> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="fraenkel.html#M2" title="FRAENKEL:mode.2">Element</a> of  <a href="fraenkel.html#K1" title="FRAENKEL:func.1">Funcs</a> <font color="Maroon" title="c1">Y</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> ;<br/>





<a NAME="E1:3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="bvfunc25.html#T2" target="_self" title="BVFUNC25:th.2">Th2</a></i>;<br/>
<a NAME="E2:3"/><b>then </b><i><font color="Green" title="E3">A1</font></i>: 
<span class="p1">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="bvfunc_1.html#T19" title="BVFUNC_1:th.19">BVFUNC_1:19</a></i>;<br/>
<a NAME="E3:3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p2">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bvfunc_1.html#K17" title="BVFUNC_1:func.17">I_el</a> <font color="Maroon" title="c1">Y</font>
 
<b>by </b><i><a class="ref" href="bvfunc_5.html#T33" title="BVFUNC_5:th.33">BVFUNC_5:33</a></i>;<br/>
<a NAME="E4:3"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="bvfunc_1.html#R1" title="BVFUNC_1:pred.1">'&lt;'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bvfunc_1.html#T19" title="BVFUNC_1:th.19">BVFUNC_1:19</a></i>;<br/>
<b>hence </b><a NAME="E5:3"/>
<font color="Maroon" title="c2">a</font> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="bvfunc_1.html#K12" title="BVFUNC_1:func.12">'imp'</a> <span class="p1">(<span class="default"><a href="valuat_1.html#K5" title="VALUAT_1:func.5">'not'</a> <font color="Maroon" title="c2">a</font></span>)</span>
 <b>by </b><i><a class="txt" href="bvfunc25.html#E2:3"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="bvfunc_1.html#T18" title="BVFUNC_1:th.18">BVFUNC_1:18</a></i>;<br/>


</div>
