Step |
Hyp |
Ref |
Expression |
1 |
|
bnj594.1 |
|
2 |
|
bnj594.2 |
|
3 |
|
bnj594.3 |
|
4 |
|
bnj594.7 |
|
5 |
|
bnj594.9 |
Could not format ( ph' <-> ( g ` (/) ) = _pred ( x , A , R ) ) : No typesetting found for |- ( ph' <-> ( g ` (/) ) = _pred ( x , A , R ) ) with typecode |- |
6 |
|
bnj594.10 |
Could not format ( ps' <-> A. i e. _om ( suc i e. n -> ( g ` suc i ) = U_ y e. ( g ` i ) _pred ( y , A , R ) ) ) : No typesetting found for |- ( ps' <-> A. i e. _om ( suc i e. n -> ( g ` suc i ) = U_ y e. ( g ` i ) _pred ( y , A , R ) ) ) with typecode |- |
7 |
|
bnj594.11 |
Could not format ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) : No typesetting found for |- ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode |- |
8 |
|
bnj594.15 |
Could not format ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
9 |
|
bnj594.16 |
Could not format ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) : No typesetting found for |- ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode |- |
10 |
|
bnj594.17 |
|
11 |
3
|
simp2bi |
|
12 |
11 1
|
sylib |
|
13 |
7
|
simp2bi |
Could not format ( ch' -> ph' ) : No typesetting found for |- ( ch' -> ph' ) with typecode |- |
14 |
13 5
|
sylib |
Could not format ( ch' -> ( g ` (/) ) = _pred ( x , A , R ) ) : No typesetting found for |- ( ch' -> ( g ` (/) ) = _pred ( x , A , R ) ) with typecode |- |
15 |
|
eqtr3 |
|
16 |
12 14 15
|
syl2an |
Could not format ( ( ch /\ ch' ) -> ( f ` (/) ) = ( g ` (/) ) ) : No typesetting found for |- ( ( ch /\ ch' ) -> ( f ` (/) ) = ( g ` (/) ) ) with typecode |- |
17 |
16
|
3adant1 |
Could not format ( ( n e. D /\ ch /\ ch' ) -> ( f ` (/) ) = ( g ` (/) ) ) : No typesetting found for |- ( ( n e. D /\ ch /\ ch' ) -> ( f ` (/) ) = ( g ` (/) ) ) with typecode |- |
18 |
|
fveq2 |
|
19 |
|
fveq2 |
|
20 |
18 19
|
eqeq12d |
|
21 |
17 20
|
syl5ibr |
Could not format ( j = (/) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( j = (/) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
22 |
21 8
|
sylibr |
|
23 |
22
|
a1d |
|
24 |
|
bnj253 |
Could not format ( ( n e. D /\ n e. D /\ ch /\ ch' ) <-> ( ( n e. D /\ n e. D ) /\ ch /\ ch' ) ) : No typesetting found for |- ( ( n e. D /\ n e. D /\ ch /\ ch' ) <-> ( ( n e. D /\ n e. D ) /\ ch /\ ch' ) ) with typecode |- |
25 |
|
bnj252 |
Could not format ( ( n e. D /\ n e. D /\ ch /\ ch' ) <-> ( n e. D /\ ( n e. D /\ ch /\ ch' ) ) ) : No typesetting found for |- ( ( n e. D /\ n e. D /\ ch /\ ch' ) <-> ( n e. D /\ ( n e. D /\ ch /\ ch' ) ) ) with typecode |- |
26 |
|
anidm |
|
27 |
26
|
3anbi1i |
Could not format ( ( ( n e. D /\ n e. D ) /\ ch /\ ch' ) <-> ( n e. D /\ ch /\ ch' ) ) : No typesetting found for |- ( ( ( n e. D /\ n e. D ) /\ ch /\ ch' ) <-> ( n e. D /\ ch /\ ch' ) ) with typecode |- |
28 |
24 25 27
|
3bitr3i |
Could not format ( ( n e. D /\ ( n e. D /\ ch /\ ch' ) ) <-> ( n e. D /\ ch /\ ch' ) ) : No typesetting found for |- ( ( n e. D /\ ( n e. D /\ ch /\ ch' ) ) <-> ( n e. D /\ ch /\ ch' ) ) with typecode |- |
29 |
|
df-bnj17 |
|
30 |
10
|
bnj1095 |
|
31 |
30
|
bnj1352 |
|
32 |
29 31
|
hbxfrbi |
|
33 |
|
bnj170 |
|
34 |
4
|
bnj923 |
|
35 |
|
elnn |
|
36 |
34 35
|
sylan2 |
|
37 |
36
|
anim1i |
|
38 |
33 37
|
sylbi |
|
39 |
|
nnsuc |
|
40 |
|
rexex |
|
41 |
38 39 40
|
3syl |
|
42 |
41
|
bnj721 |
|
43 |
32 42
|
bnj596 |
|
44 |
|
bnj667 |
|
45 |
44
|
anim1i |
|
46 |
|
bnj258 |
|
47 |
45 46
|
sylibr |
|
48 |
|
df-bnj17 |
|
49 |
|
bnj219 |
|
50 |
49
|
3ad2ant3 |
|
51 |
50
|
adantr |
|
52 |
|
vex |
|
53 |
52
|
bnj216 |
|
54 |
|
df-3an |
|
55 |
|
3anrot |
|
56 |
|
ancom |
|
57 |
54 55 56
|
3bitr3i |
|
58 |
|
eldifi |
|
59 |
58 4
|
eleq2s |
|
60 |
|
nnord |
|
61 |
|
ordtr1 |
|
62 |
59 60 61
|
3syl |
|
63 |
62
|
imp |
|
64 |
57 63
|
sylbi |
|
65 |
53 64
|
syl3an3 |
|
66 |
|
rsp |
|
67 |
10 66
|
sylbi |
|
68 |
65 67
|
mpan9 |
|
69 |
51 68
|
mpd |
|
70 |
48 69
|
sylbi |
|
71 |
70
|
anim1i |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( [. k / j ]. th /\ ( n e. D /\ ch /\ ch' ) ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( [. k / j ]. th /\ ( n e. D /\ ch /\ ch' ) ) ) with typecode |- |
72 |
|
bnj252 |
Could not format ( ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) <-> ( [. k / j ]. th /\ ( n e. D /\ ch /\ ch' ) ) ) : No typesetting found for |- ( ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) <-> ( [. k / j ]. th /\ ( n e. D /\ ch /\ ch' ) ) ) with typecode |- |
73 |
71 72
|
sylibr |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) ) with typecode |- |
74 |
|
bnj446 |
Could not format ( ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) <-> ( ( n e. D /\ ch /\ ch' ) /\ [. k / j ]. th ) ) : No typesetting found for |- ( ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) <-> ( ( n e. D /\ ch /\ ch' ) /\ [. k / j ]. th ) ) with typecode |- |
75 |
|
pm3.35 |
Could not format ( ( ( n e. D /\ ch /\ ch' ) /\ ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) -> ( f ` k ) = ( g ` k ) ) : No typesetting found for |- ( ( ( n e. D /\ ch /\ ch' ) /\ ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) -> ( f ` k ) = ( g ` k ) ) with typecode |- |
76 |
9 75
|
sylan2b |
Could not format ( ( ( n e. D /\ ch /\ ch' ) /\ [. k / j ]. th ) -> ( f ` k ) = ( g ` k ) ) : No typesetting found for |- ( ( ( n e. D /\ ch /\ ch' ) /\ [. k / j ]. th ) -> ( f ` k ) = ( g ` k ) ) with typecode |- |
77 |
74 76
|
sylbi |
Could not format ( ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) : No typesetting found for |- ( ( [. k / j ]. th /\ n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) with typecode |- |
78 |
|
iuneq1 |
|
79 |
73 77 78
|
3syl |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> U_ y e. ( f ` k ) _pred ( y , A , R ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> U_ y e. ( f ` k ) _pred ( y , A , R ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) with typecode |- |
80 |
|
bnj658 |
|
81 |
3
|
simp3bi |
|
82 |
7
|
simp3bi |
Could not format ( ch' -> ps' ) : No typesetting found for |- ( ch' -> ps' ) with typecode |- |
83 |
81 82
|
bnj240 |
Could not format ( ( n e. D /\ ch /\ ch' ) -> ( ps /\ ps' ) ) : No typesetting found for |- ( ( n e. D /\ ch /\ ch' ) -> ( ps /\ ps' ) ) with typecode |- |
84 |
80 83
|
anim12i |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( ps /\ ps' ) ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( ps /\ ps' ) ) ) with typecode |- |
85 |
|
simpl |
Could not format ( ( ps /\ ps' ) -> ps ) : No typesetting found for |- ( ( ps /\ ps' ) -> ps ) with typecode |- |
86 |
85
|
anim2i |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( ps /\ ps' ) ) -> ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( ps /\ ps' ) ) -> ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps ) ) with typecode |- |
87 |
|
simp3 |
|
88 |
87
|
anim1i |
|
89 |
|
simpl1 |
|
90 |
|
df-3an |
|
91 |
90
|
biancomi |
|
92 |
|
elnn |
|
93 |
53 36 92
|
syl2an |
|
94 |
91 93
|
sylbi |
|
95 |
2
|
bnj589 |
|
96 |
95
|
bnj590 |
|
97 |
94 96
|
mpan9 |
|
98 |
89 97
|
mpd |
|
99 |
88 98
|
syldan |
|
100 |
84 86 99
|
3syl |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( f ` j ) = U_ y e. ( f ` k ) _pred ( y , A , R ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( f ` j ) = U_ y e. ( f ` k ) _pred ( y , A , R ) ) with typecode |- |
101 |
|
simpr |
Could not format ( ( ps /\ ps' ) -> ps' ) : No typesetting found for |- ( ( ps /\ ps' ) -> ps' ) with typecode |- |
102 |
101
|
anim2i |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( ps /\ ps' ) ) -> ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps' ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( ps /\ ps' ) ) -> ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps' ) ) with typecode |- |
103 |
87
|
anim1i |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps' ) -> ( j = suc k /\ ps' ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps' ) -> ( j = suc k /\ ps' ) ) with typecode |- |
104 |
|
simpl1 |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( j = suc k /\ ps' ) ) -> j e. n ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( j = suc k /\ ps' ) ) -> j e. n ) with typecode |- |
105 |
6
|
bnj589 |
Could not format ( ps' <-> A. k e. _om ( suc k e. n -> ( g ` suc k ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) ) : No typesetting found for |- ( ps' <-> A. k e. _om ( suc k e. n -> ( g ` suc k ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) ) with typecode |- |
106 |
105
|
bnj590 |
Could not format ( ( j = suc k /\ ps' ) -> ( k e. _om -> ( j e. n -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) ) ) : No typesetting found for |- ( ( j = suc k /\ ps' ) -> ( k e. _om -> ( j e. n -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) ) ) with typecode |- |
107 |
94 106
|
mpan9 |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( j = suc k /\ ps' ) ) -> ( j e. n -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( j = suc k /\ ps' ) ) -> ( j e. n -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) ) with typecode |- |
108 |
104 107
|
mpd |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( j = suc k /\ ps' ) ) -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ( j = suc k /\ ps' ) ) -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) with typecode |- |
109 |
103 108
|
syldan |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps' ) -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k ) /\ ps' ) -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) with typecode |- |
110 |
84 102 109
|
3syl |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( g ` j ) = U_ y e. ( g ` k ) _pred ( y , A , R ) ) with typecode |- |
111 |
79 100 110
|
3eqtr4d |
Could not format ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( f ` j ) = ( g ` j ) ) : No typesetting found for |- ( ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) /\ ( n e. D /\ ch /\ ch' ) ) -> ( f ` j ) = ( g ` j ) ) with typecode |- |
112 |
111
|
ex |
Could not format ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( ( j e. n /\ n e. D /\ j = suc k /\ ta ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
113 |
47 112
|
syl |
Could not format ( ( ( j =/= (/) /\ j e. n /\ n e. D /\ ta ) /\ j = suc k ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( ( ( j =/= (/) /\ j e. n /\ n e. D /\ ta ) /\ j = suc k ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
114 |
43 113
|
bnj593 |
Could not format ( ( j =/= (/) /\ j e. n /\ n e. D /\ ta ) -> E. k ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( ( j =/= (/) /\ j e. n /\ n e. D /\ ta ) -> E. k ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
115 |
|
bnj258 |
|
116 |
|
19.9v |
Could not format ( E. k ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( E. k ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
117 |
114 115 116
|
3imtr3i |
Could not format ( ( ( j =/= (/) /\ j e. n /\ ta ) /\ n e. D ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( ( ( j =/= (/) /\ j e. n /\ ta ) /\ n e. D ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
118 |
117
|
expimpd |
Could not format ( ( j =/= (/) /\ j e. n /\ ta ) -> ( ( n e. D /\ ( n e. D /\ ch /\ ch' ) ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( ( j =/= (/) /\ j e. n /\ ta ) -> ( ( n e. D /\ ( n e. D /\ ch /\ ch' ) ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
119 |
28 118
|
syl5bir |
Could not format ( ( j =/= (/) /\ j e. n /\ ta ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( ( j =/= (/) /\ j e. n /\ ta ) -> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |- |
120 |
119 8
|
sylibr |
|
121 |
120
|
3expib |
|
122 |
23 121
|
pm2.61ine |
|