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 |
|
usgruhgr |
|
11 |
10
|
adantr |
|
12 |
11
|
adantr |
|
13 |
1
|
clnbgrssvtx |
|
14 |
3 13
|
eqsstri |
|
15 |
14
|
a1i |
|
16 |
|
eqid |
|
17 |
1 7 16 8
|
isubgredg |
|
18 |
12 15 17
|
syl2an |
|
19 |
|
f1of |
|
20 |
5
|
fveq2i |
Could not format ( Vtx ` S ) = ( Vtx ` ( StarGr ` N ) ) : No typesetting found for |- ( Vtx ` S ) = ( Vtx ` ( StarGr ` N ) ) with typecode |- |
21 |
|
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 |- |
22 |
4 21
|
ax-mp |
Could not format ( Vtx ` ( StarGr ` N ) ) = ( 0 ... N ) : No typesetting found for |- ( Vtx ` ( StarGr ` N ) ) = ( 0 ... N ) with typecode |- |
23 |
6 20 22
|
3eqtri |
|
24 |
23
|
eqimssi |
|
25 |
24
|
a1i |
|
26 |
19 25
|
fssd |
|
27 |
26
|
ad2antrl |
|
28 |
27
|
adantr |
|
29 |
28
|
fimassd |
|
30 |
|
simplll |
|
31 |
|
simpl |
|
32 |
1 7
|
usgredg |
|
33 |
30 31 32
|
syl2an |
|
34 |
|
vex |
|
35 |
|
vex |
|
36 |
34 35
|
prss |
|
37 |
|
elclnbgrelnbgr |
|
38 |
37
|
expcom |
|
39 |
3
|
eleq2i |
|
40 |
2
|
eleq2i |
|
41 |
38 39 40
|
3imtr4g |
|
42 |
|
elclnbgrelnbgr |
|
43 |
42
|
expcom |
|
44 |
3
|
eleq2i |
|
45 |
2
|
eleq2i |
|
46 |
43 44 45
|
3imtr4g |
|
47 |
41 46
|
im2anan9r |
|
48 |
47
|
imp |
|
49 |
48
|
3adant3 |
|
50 |
|
preq1 |
|
51 |
|
eqidd |
|
52 |
50 51
|
neleq12d |
|
53 |
|
preq2 |
|
54 |
|
eqidd |
|
55 |
53 54
|
neleq12d |
|
56 |
52 55
|
rspc2v |
|
57 |
49 56
|
syl |
|
58 |
|
pm2.24nel |
|
59 |
58
|
adantl |
|
60 |
59
|
3ad2ant3 |
|
61 |
57 60
|
syld |
|
62 |
61
|
3exp |
|
63 |
62
|
com24 |
|
64 |
63
|
adantld |
|
65 |
64
|
adantld |
|
66 |
65
|
adantrd |
|
67 |
66
|
imp4c |
|
68 |
|
simpl |
|
69 |
|
simpllr |
|
70 |
69
|
adantl |
|
71 |
|
simplrl |
|
72 |
71
|
necomd |
|
73 |
72
|
adantl |
|
74 |
|
simprrr |
|
75 |
|
simprrl |
|
76 |
1 2 3 4 5 6 7
|
isubgr3stgrlem4 |
|
77 |
68 70 73 74 75 76
|
syl113anc |
|
78 |
|
prcom |
|
79 |
78
|
imaeq2i |
|
80 |
79
|
eqeq1i |
|
81 |
80
|
rexbii |
|
82 |
77 81
|
sylibr |
|
83 |
82
|
ex |
|
84 |
|
simpl |
|
85 |
69
|
adantl |
|
86 |
71
|
adantl |
|
87 |
|
simprrl |
|
88 |
|
simprrr |
|
89 |
1 2 3 4 5 6 7
|
isubgr3stgrlem4 |
|
90 |
84 85 86 87 88 89
|
syl113anc |
|
91 |
90
|
ex |
|
92 |
67 83 91
|
pm2.61iine |
|
93 |
92
|
ex |
|
94 |
36 93
|
biimtrrid |
|
95 |
94
|
exp32 |
|
96 |
95
|
adantrd |
|
97 |
96
|
imp |
|
98 |
97
|
com23 |
|
99 |
|
sseq1 |
|
100 |
|
eleq1 |
|
101 |
|
imaeq2 |
|
102 |
101
|
eqeq1d |
|
103 |
102
|
rexbidv |
|
104 |
100 103
|
imbi12d |
|
105 |
99 104
|
imbi12d |
|
106 |
105
|
adantl |
|
107 |
106
|
adantl |
|
108 |
98 107
|
mpbird |
|
109 |
108
|
ex |
|
110 |
109
|
com24 |
|
111 |
110
|
imp32 |
|
112 |
111
|
a1d |
|
113 |
112
|
rexlimdvv |
|
114 |
33 113
|
mpd |
|
115 |
|
stgredgel |
Could not format ( N e. NN0 -> ( ( F " i ) e. ( Edg ` ( StarGr ` N ) ) <-> ( ( F " i ) C_ ( 0 ... N ) /\ E. z e. ( 1 ... N ) ( F " i ) = { 0 , z } ) ) ) : No typesetting found for |- ( N e. NN0 -> ( ( F " i ) e. ( Edg ` ( StarGr ` N ) ) <-> ( ( F " i ) C_ ( 0 ... N ) /\ E. z e. ( 1 ... N ) ( F " i ) = { 0 , z } ) ) ) with typecode |- |
116 |
4 115
|
ax-mp |
Could not format ( ( F " i ) e. ( Edg ` ( StarGr ` N ) ) <-> ( ( F " i ) C_ ( 0 ... N ) /\ E. z e. ( 1 ... N ) ( F " i ) = { 0 , z } ) ) : No typesetting found for |- ( ( F " i ) e. ( Edg ` ( StarGr ` N ) ) <-> ( ( F " i ) C_ ( 0 ... N ) /\ E. z e. ( 1 ... N ) ( F " i ) = { 0 , z } ) ) with typecode |- |
117 |
29 114 116
|
sylanbrc |
Could not format ( ( ( ( ( G e. USGraph /\ X e. V ) /\ ( ( # ` U ) = N /\ A. x e. U A. y e. U { x , y } e/ E ) ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) /\ ( i e. E /\ i C_ C ) ) -> ( F " i ) e. ( Edg ` ( StarGr ` N ) ) ) : No typesetting found for |- ( ( ( ( ( G e. USGraph /\ X e. V ) /\ ( ( # ` U ) = N /\ A. x e. U A. y e. U { x , y } e/ E ) ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) /\ ( i e. E /\ i C_ C ) ) -> ( F " i ) e. ( Edg ` ( StarGr ` N ) ) ) with typecode |- |
118 |
18 117
|
sylbida |
Could not format ( ( ( ( ( G e. USGraph /\ X e. V ) /\ ( ( # ` U ) = N /\ A. x e. U A. y e. U { x , y } e/ E ) ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) /\ i e. I ) -> ( F " i ) e. ( Edg ` ( StarGr ` N ) ) ) : No typesetting found for |- ( ( ( ( ( G e. USGraph /\ X e. V ) /\ ( ( # ` U ) = N /\ A. x e. U A. y e. U { x , y } e/ E ) ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) /\ i e. I ) -> ( F " i ) e. ( Edg ` ( StarGr ` N ) ) ) with typecode |- |
119 |
118 9
|
fmptd |
Could not format ( ( ( ( G e. USGraph /\ X e. V ) /\ ( ( # ` U ) = N /\ A. x e. U A. y e. U { x , y } e/ E ) ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) -> H : I --> ( Edg ` ( StarGr ` N ) ) ) : No typesetting found for |- ( ( ( ( G e. USGraph /\ X e. V ) /\ ( ( # ` U ) = N /\ A. x e. U A. y e. U { x , y } e/ E ) ) /\ ( F : C -1-1-onto-> W /\ ( F ` X ) = 0 ) ) -> H : I --> ( Edg ` ( StarGr ` N ) ) ) with typecode |- |