| 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 |- |