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<div><span class="kw">theorem </span><a NAME="T52"><span class="comment"><font color="firebrick">:: BCIALG_5:52</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="bcialg_5.html#V1" title="BCIALG_5:attr.1">quasi-commutative</a>  <a href="bcialg_1.html#NM2" title="BCIALG_1:NM.2">BCK-algebra</a> holds <br/> ( <font color="Olive" title="b1">X</font> is   <a href="bcialg_5.html#NM2" title="BCIALG_5:NM.2">BCK-algebra</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ,1, <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ,1 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> <span class="p1">(<span class="default"><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></span>)</span> <a href="bcialg_1.html#K1" title="BCIALG_1:func.1">\</a> <font color="Olive" title="b3">y</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="bcialg_3.html#T28" onmouseover="rs('bcialg_3/T28')" onmouseout="rh()">BCIALG_3:28</a>, <a class="ref" href="bcialg_5.html#T49" target="_self" onmouseover="rs('bcialg_5/T49')" onmouseout="rh()">Th49</a></span>;<br/></div></div>
