$( Modified version of demo0.mm from 1-Jan-04 $) $( PUBLIC DOMAIN DEDICATION This file is placed in the public domain per the Creative Commons Public Domain Dedication. http://creativecommons.org/licenses/publicdomain/ Norman Megill - email: nm at alum.mit.edu $) $c 0 + = -> ( ) term wff |- $. $v t r s P Q $. tt $f term t $. tr $f term r $. ts $f term s $. wp $f wff P $. wq $f wff Q $. tze $a term 0 $. tpl $a term ( t + r ) $. weq $a wff t = r $. wim $a wff ( P -> Q ) $. a1 $a |- ( t = r -> ( t = s -> r = s ) ) $. a2 $a |- ( t + 0 ) = t $. ${ $( Define the modus ponens inference rule $) min $e |- P $. maj $e |- ( P -> Q ) $. mp $a |- Q $. $} th1 $p |- t = t $= $( Here is its proof: $) tt tze tpl tt weq tt tt weq tt a2 tt tze tpl tt weq tt tze tpl tt weq tt tt weq wim tt a2 tt tze tpl tt tt a1 mp mp $.