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<span class="kw">let </span><font color="Maroon" title="c3">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">R</font> is <font color="Maroon" title="c2">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  implies <font color="Maroon" title="c3">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:125_1_1"/>
<font color="Maroon" title="c3">R</font> is <font color="Maroon" title="c2">X</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a> </span><br/>

<a NAME="E2:125_1_1"/><span class="kw">then </span>
(  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Y</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/>
<a NAME="E3:125_1_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c3">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:125_1_1"/>
<font color="Maroon" title="c3">R</font> is <font color="Maroon" title="c1">Y</font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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