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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</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">H</font> is  <a href="zf_lang.html#V10" title="ZF_LANG:attr.10">biconditional</a>  implies (  <a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K26" title="ZF_LANG:func.26">the_consequent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> &amp;  <a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K25" title="ZF_LANG:func.25">the_antecedent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:21"/>
<font color="Maroon" title="c1">H</font> is  <a href="zf_lang.html#V10" title="ZF_LANG:attr.10">biconditional</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K26" title="ZF_LANG:func.26">the_consequent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> &amp;  <a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K25" title="ZF_LANG:func.25">the_antecedent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> )</span><br/>

<a NAME="E2:21"/><span class="kw">then </span>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K27" title="ZF_LANG:func.27">the_left_side_of</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang.html#T49" title="ZF_LANG:th.49">ZF_LANG:49</a></span>;<br/>
<a NAME="E3:21"/><span class="kw">then </span>
(  <a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K27" title="ZF_LANG:func.27">the_left_side_of</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font></span>)</span> &amp;  <a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="zf_lang.html#K11" title="ZF_LANG:func.11">=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K27" title="ZF_LANG:func.27">the_left_side_of</a> <font color="Maroon" title="c1">H</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T4" target="_self" title="ZF_LANG1:th.4">Th4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:21"/>
(  <a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K26" title="ZF_LANG:func.26">the_consequent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K21" title="ZF_LANG:func.21">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> &amp;  <a href="zf_lang.html#K28" title="ZF_LANG:func.28">the_right_side_of</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_lang.html#K25" title="ZF_LANG:func.25">the_antecedent_of</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K22" title="ZF_LANG:func.22">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zf_lang1.html#T6" target="_self" title="ZF_LANG1:th.6">Th6</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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