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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="modal_1.html#NM5">MP-wff</a>;<br/>

<a NAME="E1:69"/><i><font color="Green">E52</font></i>: 
(  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0 or  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 or  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 )
 
<b>by </b><i><a class="ref" href="cqc_the1.html#T3">CQC_THE1:3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="69_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:69_1_1"/>
(  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 or  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2 )
 </span><b>by </b><i><a class="txt" href="modal_1.html#E1:69"><i><font color="Green">E52</font></i></a>, <a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_1"><b>suppose </b></a><a NAME="E1:69_1_1_1"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_1_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K17" target="_self">VERUM</a>  or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM1">MP-variable</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K16" target="_self">@</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K10" target="_self">'not'</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K11" target="_self">(#)</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="modal_1.html#K12" target="_self">'&amp;'</a> <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="modal_1.html#T42" target="_self">Th42</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="69_1_1_2"><b>suppose </b></a><a NAME="E1:69_1_1_2"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 2
 ;<br/><div class="add"><b>hence </b><a NAME="E2:69_1_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K17" target="_self">VERUM</a>  or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM1">MP-variable</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K16" target="_self">@</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K10" target="_self">'not'</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K11" target="_self">(#)</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="modal_1.html#K12" target="_self">'&amp;'</a> <font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="modal_1.html#T43" target="_self">Th43</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:69"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K17" target="_self">VERUM</a>  or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM1">MP-variable</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K16" target="_self">@</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K10" target="_self">'not'</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="modal_1.html#K11" target="_self">(#)</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="modal_1.html#NM5">MP-wff</a> st <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="modal_1.html#K12" target="_self">'&amp;'</a> <font color="Olive">b<sub>2</sub></font> )
 ;<br/>


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