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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E56">Th54</font></span>: <a NAME="T54"><span class="comment"><font color="firebrick">:: QUOFIELD:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</font>, <font color="Olive" title="b3">T</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font>  st <font color="Olive" title="b4">f</font> is  <a href="quofield.html#NV1" title="QUOFIELD:NV.1">RingHomomorphism</a>  holds <br/> for <font color="Olive" title="b5">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b2">S</font>,<font color="Olive" title="b3">T</font>  st <font color="Olive" title="b5">g</font> is  <a href="quofield.html#NV1" title="QUOFIELD:NV.1">RingHomomorphism</a>  holds <br/><font color="Olive" title="b5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b4">f</font> is  <a href="quofield.html#NV1" title="QUOFIELD:NV.1">RingHomomorphism</a> </div></div>
