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0001 <!DOCTYPE html> 0002 <html><head> 0003 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/> 0004 <title>test.mm</title> 0005 <meta name="generator" content="KF5::SyntaxHighlighting - Definition (Metamath) - Theme (Breeze Light)"/> 0006 </head><body style="background-color:#ffffff;color:#1f1c1b"><pre> 0007 <span style="color:#898887">$( Modified version of demo0.mm from 1-Jan-04 $)</span> 0008 0009 <span style="color:#898887">$(</span> 0010 <span style="color:#898887"> PUBLIC DOMAIN DEDICATION</span> 0011 0012 <span style="color:#898887">This file is placed in the public domain per the Creative Commons Public</span> 0013 <span style="color:#898887">Domain Dedication. http://creativecommons.org/licenses/publicdomain/</span> 0014 0015 <span style="color:#898887">Norman Megill - email: nm at alum.mit.edu</span> 0016 <span style="color:#898887">$)</span> 0017 0018 <span style="font-weight:bold">$c</span><span style="color:#644a9b"> 0 + = -> ( ) term wff |- </span><span style="font-weight:bold">$.</span> 0019 0020 <span style="font-weight:bold">$v</span><span style="color:#0057ae"> t r s P Q </span><span style="font-weight:bold">$.</span> 0021 0022 <span style="color:#ff5500">tt</span> <span style="font-weight:bold">$f</span> <span style="color:#644a9b">term</span><span style="color:#0057ae"> t </span><span style="font-weight:bold">$.</span> 0023 <span style="color:#ff5500">tr</span> <span style="font-weight:bold">$f</span> <span style="color:#644a9b">term</span><span style="color:#0057ae"> r </span><span style="font-weight:bold">$.</span> 0024 <span style="color:#ff5500">ts</span> <span style="font-weight:bold">$f</span> <span style="color:#644a9b">term</span><span style="color:#0057ae"> s </span><span style="font-weight:bold">$.</span> 0025 <span style="color:#ff5500">wp</span> <span style="font-weight:bold">$f</span> <span style="color:#644a9b">wff</span><span style="color:#0057ae"> P </span><span style="font-weight:bold">$.</span> 0026 <span style="color:#ff5500">wq</span> <span style="font-weight:bold">$f</span> <span style="color:#644a9b">wff</span><span style="color:#0057ae"> Q </span><span style="font-weight:bold">$.</span> 0027 0028 <span style="color:#ff5500">tze</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">term</span><span style="color:#0057ae"> 0 </span><span style="font-weight:bold">$.</span> 0029 <span style="color:#ff5500">tpl</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">term</span><span style="color:#0057ae"> ( t + r ) </span><span style="font-weight:bold">$.</span> 0030 0031 <span style="color:#ff5500">weq</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">wff</span><span style="color:#0057ae"> t = r </span><span style="font-weight:bold">$.</span> 0032 <span style="color:#ff5500">wim</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">wff</span><span style="color:#0057ae"> ( P -> Q ) </span><span style="font-weight:bold">$.</span> 0033 0034 <span style="color:#ff5500">a1</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">|-</span><span style="color:#0057ae"> ( t = r -> ( t = s -> r = s ) ) </span><span style="font-weight:bold">$.</span> 0035 <span style="color:#ff5500">a2</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">|-</span><span style="color:#0057ae"> ( t + 0 ) = t </span><span style="font-weight:bold">$.</span> 0036 <span style="font-weight:bold">${</span> 0037 <span style="color:#898887">$( Define the modus ponens inference rule $)</span> 0038 <span style="color:#ff5500">min</span> <span style="font-weight:bold">$e</span> <span style="color:#644a9b">|-</span><span style="color:#0057ae"> P </span><span style="font-weight:bold">$.</span> 0039 <span style="color:#ff5500">maj</span> <span style="font-weight:bold">$e</span> <span style="color:#644a9b">|-</span><span style="color:#0057ae"> ( P -> Q ) </span><span style="font-weight:bold">$.</span> 0040 <span style="color:#ff5500">mp</span> <span style="font-weight:bold">$a</span> <span style="color:#644a9b">|-</span><span style="color:#0057ae"> Q </span><span style="font-weight:bold">$.</span> 0041 <span style="font-weight:bold">$}</span> 0042 0043 <span style="color:#ff5500">th1</span> <span style="font-weight:bold">$p</span> <span style="color:#644a9b">|-</span><span style="color:#0057ae"> t = t </span><span style="font-weight:bold">$=</span> 0044 <span style="color:#ff5500"> </span><span style="color:#898887">$( Here is its proof: $)</span> 0045 <span style="color:#ff5500"> tt tze tpl tt weq tt tt weq tt a2 tt tze tpl</span> 0046 <span style="color:#ff5500"> tt weq tt tze tpl tt weq tt tt weq wim tt a2</span> 0047 <span style="color:#ff5500"> tt tze tpl tt tt a1 mp mp</span> 0048 <span style="font-weight:bold">$.</span> 0049 </pre></body></html>