Step |
Hyp |
Ref |
Expression |
1 |
|
isubgr3stgr.v |
|
2 |
|
isubgr3stgr.u |
|
3 |
|
isubgr3stgr.c |
|
4 |
|
isubgr3stgr.n |
|
5 |
|
isubgr3stgr.s |
Could not format S = ( StarGr ` N ) : No typesetting found for |- S = ( StarGr ` N ) with typecode |- |
6 |
|
isubgr3stgr.w |
|
7 |
|
isubgr3stgr.e |
|
8 |
|
isubgr3stgr.i |
|
9 |
|
isubgr3stgr.h |
|
10 |
|
stgredgel |
Could not format ( N e. NN0 -> ( J e. ( Edg ` ( StarGr ` N ) ) <-> ( J C_ ( 0 ... N ) /\ E. y e. ( 1 ... N ) J = { 0 , y } ) ) ) : No typesetting found for |- ( N e. NN0 -> ( J e. ( Edg ` ( StarGr ` N ) ) <-> ( J C_ ( 0 ... N ) /\ E. y e. ( 1 ... N ) J = { 0 , y } ) ) ) with typecode |- |
11 |
4 10
|
mp1i |
Could not format ( ( ( G e. USGraph /\ X e. V ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) -> ( J e. ( Edg ` ( StarGr ` N ) ) <-> ( J C_ ( 0 ... N ) /\ E. y e. ( 1 ... N ) J = { 0 , y } ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ X e. V ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) -> ( J e. ( Edg ` ( StarGr ` N ) ) <-> ( J C_ ( 0 ... N ) /\ E. y e. ( 1 ... N ) J = { 0 , y } ) ) ) with typecode |- |
12 |
|
c0ex |
|
13 |
12
|
a1i |
|
14 |
|
prssg |
|
15 |
13 14
|
sylan |
|
16 |
|
f1ocnv |
|
17 |
|
f1ofn |
|
18 |
5
|
fveq2i |
Could not format ( Vtx ` S ) = ( Vtx ` ( StarGr ` N ) ) : No typesetting found for |- ( Vtx ` S ) = ( Vtx ` ( StarGr ` N ) ) with typecode |- |
19 |
|
stgrvtx |
Could not format ( N e. NN0 -> ( Vtx ` ( StarGr ` N ) ) = ( 0 ... N ) ) : No typesetting found for |- ( N e. NN0 -> ( Vtx ` ( StarGr ` N ) ) = ( 0 ... N ) ) with typecode |- |
20 |
4 19
|
ax-mp |
Could not format ( Vtx ` ( StarGr ` N ) ) = ( 0 ... N ) : No typesetting found for |- ( Vtx ` ( StarGr ` N ) ) = ( 0 ... N ) with typecode |- |
21 |
6 18 20
|
3eqtri |
|
22 |
21
|
fneq2i |
|
23 |
17 22
|
sylib |
|
24 |
16 23
|
syl |
|
25 |
24
|
ad2antrl |
|
26 |
25
|
adantr |
|
27 |
26
|
anim1i |
|
28 |
|
3anass |
|
29 |
27 28
|
sylibr |
|
30 |
29
|
ex |
|
31 |
15 30
|
sylbird |
|
32 |
31
|
imp |
|
33 |
|
fnimapr |
|
34 |
32 33
|
syl |
|
35 |
1
|
clnbgrvtxel |
|
36 |
35
|
adantl |
|
37 |
36 3
|
eleqtrrdi |
|
38 |
|
simpl |
|
39 |
37 38
|
anim12ci |
|
40 |
|
simprr |
|
41 |
39 40
|
jca |
|
42 |
41
|
adantr |
|
43 |
|
f1ocnvfv |
|
44 |
43
|
imp |
|
45 |
42 44
|
syl |
|
46 |
35 3
|
eleqtrrdi |
|
47 |
46
|
ad3antlr |
|
48 |
|
f1of |
|
49 |
16 48
|
syl |
|
50 |
49
|
ad2antrl |
|
51 |
50
|
adantr |
|
52 |
|
fz1ssfz0 |
|
53 |
52
|
sseli |
|
54 |
53 21
|
eleqtrrdi |
|
55 |
54
|
adantl |
|
56 |
51 55
|
ffvelcdmd |
|
57 |
47 56
|
jca |
|
58 |
3
|
eleq2i |
|
59 |
|
usgrupgr |
|
60 |
59
|
anim1i |
|
61 |
60
|
ad2antrr |
|
62 |
1
|
clnbgrssvtx |
|
63 |
3 62
|
eqsstri |
|
64 |
63 56
|
sselid |
|
65 |
|
df-3an |
|
66 |
61 64 65
|
sylanbrc |
|
67 |
66
|
ad2antrr |
|
68 |
1 7
|
clnbupgrel |
|
69 |
67 68
|
syl |
|
70 |
58 69
|
bitrid |
|
71 |
|
eqeq2 |
|
72 |
71
|
adantl |
|
73 |
|
f1of1 |
|
74 |
16 73
|
syl |
|
75 |
74
|
ad2antrl |
|
76 |
|
0elfz |
|
77 |
4 76
|
ax-mp |
|
78 |
77 21
|
eleqtrri |
|
79 |
54 78
|
jctir |
|
80 |
|
f1veqaeq |
|
81 |
75 79 80
|
syl2an |
|
82 |
|
elfznn |
|
83 |
|
nnne0 |
|
84 |
|
eqneqall |
|
85 |
83 84
|
syl5com |
|
86 |
82 85
|
syl |
|
87 |
86
|
adantl |
|
88 |
81 87
|
syld |
|
89 |
88
|
adantr |
|
90 |
72 89
|
sylbird |
|
91 |
90
|
adantr |
|
92 |
|
prcom |
|
93 |
92
|
eleq1i |
|
94 |
93
|
biimpi |
|
95 |
94
|
a1i |
|
96 |
91 95
|
jaod |
|
97 |
70 96
|
sylbid |
|
98 |
97
|
impr |
|
99 |
|
prssi |
|
100 |
99
|
adantl |
|
101 |
98 100
|
jca |
|
102 |
57 101
|
mpidan |
|
103 |
|
preq1 |
|
104 |
103
|
eleq1d |
|
105 |
103
|
sseq1d |
|
106 |
104 105
|
anbi12d |
|
107 |
106
|
adantl |
|
108 |
102 107
|
mpbird |
|
109 |
45 108
|
mpdan |
|
110 |
109
|
adantr |
|
111 |
|
usgruhgr |
|
112 |
111
|
ad3antrrr |
|
113 |
63
|
a1i |
|
114 |
|
eqid |
|
115 |
1 7 114 8
|
isubgredg |
|
116 |
112 113 115
|
syl2an |
|
117 |
110 116
|
mpbird |
|
118 |
34 117
|
eqeltrd |
|
119 |
118
|
ex |
|
120 |
|
sseq1 |
|
121 |
|
imaeq2 |
|
122 |
121
|
eleq1d |
|
123 |
120 122
|
imbi12d |
|
124 |
119 123
|
syl5ibrcom |
|
125 |
124
|
rexlimdva |
|
126 |
125
|
impcomd |
|
127 |
11 126
|
sylbid |
Could not format ( ( ( G e. USGraph /\ X e. V ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) -> ( J e. ( Edg ` ( StarGr ` N ) ) -> ( `' F " J ) e. I ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ X e. V ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) -> ( J e. ( Edg ` ( StarGr ` N ) ) -> ( `' F " J ) e. I ) ) with typecode |- |
128 |
127
|
3impia |
Could not format ( ( ( G e. USGraph /\ X e. V ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) /\ J e. ( Edg ` ( StarGr ` N ) ) ) -> ( `' F " J ) e. I ) : No typesetting found for |- ( ( ( G e. USGraph /\ X e. V ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) /\ J e. ( Edg ` ( StarGr ` N ) ) ) -> ( `' F " J ) e. I ) with typecode |- |