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<span class="kw">let </span><font color="Maroon" title="c1">X</font>, <font color="Maroon" title="c2">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</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="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c2">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:13"/>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font>
 ; <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="c2">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E2:13"/><span class="kw">then </span>
 for <font color="Olive" title="b1">p</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">CQC-WFF</a>   st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Maroon" title="c2">Y</font> <a href="cqc_the1.html#R3" title="CQC_THE1:pred.3">|-</a> <font color="Olive" title="b1">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#T1" target="_self" title="CQC_THE3:th.1">Th1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13"/>
<font color="Maroon" title="c2">Y</font> <a href="cqc_the3.html#R2" title="CQC_THE3:pred.2">|-</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cqc_the3.html#D2" target="_self" title="CQC_THE3:def.2">Def2</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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