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<b>let </b><font color="Maroon" title="c1">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()  st <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c1">s</font>,<font color="Olive" title="b1">t</font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c1">s</font>,<font color="Olive" title="b1">t</font>)]</span><br/><b>let </b><font color="Maroon" title="c2">t</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>(); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>] implies <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)] )</span><br/>



<b>assume </b><a NAME="E1:14_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)]</span><br/>

<a NAME="E2:14_1"/><b>then </b>
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>) where <font color="Olive" title="b1">s1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>(), <font color="Olive" title="b2">t1</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">s1</font>,<font color="Olive" title="b2">t1</font>] </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E3:14_1"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>)]
 <b>by </b><i><a class="txt" href="fraenkel.html#E1:14"><i><font color="Green" title="E4">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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