1$( Modified version of demo0.mm from 1-Jan-04 $)
2
3$(
4                      PUBLIC DOMAIN DEDICATION
5
6This file is placed in the public domain per the Creative Commons Public
7Domain Dedication. http://creativecommons.org/licenses/publicdomain/
8
9Norman Megill - email: nm at alum.mit.edu
10$)
11
12$c 0 + = -> ( ) term wff |- $.
13
14$v t r s P Q $.
15
16tt $f term t $.
17tr $f term r $.
18ts $f term s $.
19wp $f wff P $.
20wq $f wff Q $.
21
22tze $a term 0 $.
23tpl $a term ( t + r ) $.
24
25weq $a wff t = r $.
26wim $a wff ( P -> Q ) $.
27
28a1 $a |- ( t = r -> ( t = s -> r = s ) ) $.
29a2 $a |- ( t + 0 ) = t $.
30${
31    $( Define the modus ponens inference rule $)
32    min $e |- P $.
33    maj $e |- ( P -> Q ) $.
34    mp  $a |- Q $.
35$}
36
37th1 $p |- t = t $=
38    $( Here is its proof: $)
39    tt tze tpl tt weq tt tt weq tt a2 tt tze tpl
40    tt weq tt tze tpl tt weq tt tt weq wim tt a2
41    tt tze tpl tt tt a1 mp mp
42$.
43