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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: BCIIDEAL:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bcialg_1.html#NM2" title="BCIALG_1:NM.2">BCK-algebra</a> holds <br/> ( <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">X</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> is   <a href="bciideal.html#V3" title="BCIIDEAL:attr.3">commutative</a>   <a href="bcialg_1.html#M2" title="BCIALG_1:mode.2">Ideal</a> of <font color="Olive" title="b1">X</font> iff  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font> holds  <font color="Olive" title="b2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">y</font> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b2">x</font></span>)</span></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_3.html#T3" onmouseover="rs('bcialg_3/T3')" onmouseout="rh()">BCIALG_3:3</a>, <a class="ref" href="bciideal.html#T36" target="_self" onmouseover="rs('bciideal/T36')" onmouseout="rh()">Th36</a></span>;<br/></div></div>
