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<div><span class="kw">theorem </span><a NAME="T53"><span class="comment"><font color="firebrick">:: ARMSTRNG:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#V3" title="ARMSTRNG:attr.3">(F1)</a>  &amp; <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#NV4" title="ARMSTRNG:NV.4">(F2)</a>  &amp; <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#V4" title="ARMSTRNG:attr.4">(F3)</a>  &amp; <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#V5" title="ARMSTRNG:attr.5">(F4)</a>  iff ( <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#NV5" title="ARMSTRNG:NV.5">(DC1)</a>  &amp; <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#V7" title="ARMSTRNG:attr.7">(DC3)</a>  &amp; <font color="Olive" title="b2">F</font> is  <a href="armstrng.html#V12" title="ARMSTRNG:attr.12">(DC4)</a>  ) )</div></div>
