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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bcialg_1.html#NM1" title="BCIALG_1:NM.1">BCI-algebra</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">X</font> is <a href="bcialg_1.html#V20" title="BCIALG_1:attr.20">alternative</a> implies <font color="Maroon" title="c1">X</font> is <a href="bcialg_1.html#V17" title="BCIALG_1:attr.17">implicative</a> )</span><br/>

<b>assume </b><a NAME="E1:132"/>
<font color="Maroon" title="c1">X</font> is <a href="bcialg_1.html#V20" title="BCIALG_1:attr.20">alternative</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">X</font> is <a href="bcialg_1.html#V17" title="BCIALG_1:attr.17">implicative</a></span><br/>

<a NAME="E2:132"/><b>then </b>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b2">y</font></span>)</span></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b1">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="bcialg_1.html#T76" target="_self" title="BCIALG_1:th.76">Th76</a></i>;<br/>
<b>hence </b><a NAME="E3:132"/>
<font color="Maroon" title="c1">X</font> is <a href="bcialg_1.html#V17" title="BCIALG_1:attr.17">implicative</a>
 <b>by </b><i><a class="ref" href="bcialg_1.html#D24" target="_self" title="BCIALG_1:def.24">Def24</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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