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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: FUNCT_2:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font> holds <br/> ( (  for <font color="Olive" title="b4">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Y</font> holds <br/><font color="Olive" title="b3">f</font> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) iff  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">Y</font> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T73" onmouseover="rs('funct_1/T73')" onmouseout="rh()">FUNCT_1:73</a>, <a class="ref" href="funct_1.html#T72" onmouseover="rs('funct_1/T72')" onmouseout="rh()">FUNCT_1:72</a></span>;<br/></div></div>
