Step |
Hyp |
Ref |
Expression |
1 |
|
clnbgr3stgrgrlic.n |
|
2 |
|
clnbgr3stgrgrlic.v |
|
3 |
|
clnbgr3stgrgrlic.w |
|
4 |
2
|
fvexi |
|
5 |
3
|
fvexi |
|
6 |
4 5
|
pm3.2i |
|
7 |
|
breng |
|
8 |
6 7
|
mp1i |
|
9 |
|
usgruhgr |
|
10 |
9
|
adantl |
|
11 |
10
|
3ad2ant1 |
Could not format ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> H e. UHGraph ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> H e. UHGraph ) with typecode |- |
12 |
3
|
clnbgrssvtx |
|
13 |
12
|
a1i |
Could not format ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( H ClNeighbVtx ( f ` x ) ) C_ W ) : No typesetting found for |- ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( H ClNeighbVtx ( f ` x ) ) C_ W ) with typecode |- |
14 |
3
|
isubgruhgr |
|
15 |
11 13 14
|
syl2an2r |
Could not format ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) e. UHGraph ) : No typesetting found for |- ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) e. UHGraph ) with typecode |- |
16 |
|
f1of |
|
17 |
16
|
3ad2ant2 |
|
18 |
|
simp3 |
|
19 |
17 18
|
ffvelcdmd |
|
20 |
|
oveq2 |
|
21 |
20
|
oveq2d |
|
22 |
21
|
breq1d |
Could not format ( y = ( f ` x ) -> ( ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) <-> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) : No typesetting found for |- ( y = ( f ` x ) -> ( ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) <-> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) with typecode |- |
23 |
22
|
rspcv |
Could not format ( ( f ` x ) e. W -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) : No typesetting found for |- ( ( f ` x ) e. W -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) with typecode |- |
24 |
19 23
|
syl |
Could not format ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ x e. V ) -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ x e. V ) -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) with typecode |- |
25 |
24
|
3exp |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( f : V -1-1-onto-> W -> ( x e. V -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( f : V -1-1-onto-> W -> ( x e. V -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) ) ) with typecode |- |
26 |
25
|
com34 |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( f : V -1-1-onto-> W -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( x e. V -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( f : V -1-1-onto-> W -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( x e. V -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) ) ) ) with typecode |- |
27 |
26
|
3imp1 |
Could not format ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) : No typesetting found for |- ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) ) with typecode |- |
28 |
|
gricsym |
Could not format ( ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) e. UHGraph -> ( ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) -> ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) : No typesetting found for |- ( ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) e. UHGraph -> ( ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ~=gr ( StarGr ` N ) -> ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) with typecode |- |
29 |
15 27 28
|
sylc |
Could not format ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) : No typesetting found for |- ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) with typecode |- |
30 |
29
|
anim1ci |
Could not format ( ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) /\ ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) ) -> ( ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) /\ ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) ) -> ( ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) with typecode |- |
31 |
|
grictr |
Could not format ( ( ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) -> ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) : No typesetting found for |- ( ( ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ ( StarGr ` N ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) -> ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) with typecode |- |
32 |
30 31
|
syl |
Could not format ( ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) /\ ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) ) -> ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) : No typesetting found for |- ( ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) /\ ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) ) -> ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) with typecode |- |
33 |
32
|
ex |
Could not format ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) : No typesetting found for |- ( ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) /\ x e. V ) -> ( ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) with typecode |- |
34 |
33
|
ralimdva |
Could not format ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph ) /\ f : V -1-1-onto-> W /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) with typecode |- |
35 |
34
|
3exp |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( f : V -1-1-onto-> W -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( f : V -1-1-onto-> W -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) with typecode |- |
36 |
35
|
com24 |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( f : V -1-1-onto-> W -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) -> ( A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) -> ( f : V -1-1-onto-> W -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) with typecode |- |
37 |
36
|
imp32 |
Could not format ( ( ( G e. USGraph /\ H e. USGraph ) /\ ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) ) -> ( f : V -1-1-onto-> W -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph ) /\ ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) ) -> ( f : V -1-1-onto-> W -> A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) with typecode |- |
38 |
37
|
ancld |
Could not format ( ( ( G e. USGraph /\ H e. USGraph ) /\ ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) ) -> ( f : V -1-1-onto-> W -> ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph ) /\ ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) ) -> ( f : V -1-1-onto-> W -> ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) with typecode |- |
39 |
38
|
eximdv |
Could not format ( ( ( G e. USGraph /\ H e. USGraph ) /\ ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) ) -> ( E. f f : V -1-1-onto-> W -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph ) /\ ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) ) -> ( E. f f : V -1-1-onto-> W -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) with typecode |- |
40 |
39
|
ex |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> ( E. f f : V -1-1-onto-> W -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> ( E. f f : V -1-1-onto-> W -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) with typecode |- |
41 |
40
|
com23 |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( E. f f : V -1-1-onto-> W -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( E. f f : V -1-1-onto-> W -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) with typecode |- |
42 |
8 41
|
sylbid |
Could not format ( ( G e. USGraph /\ H e. USGraph ) -> ( V ~~ W -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph ) -> ( V ~~ W -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) ) with typecode |- |
43 |
42
|
3impia |
Could not format ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) : No typesetting found for |- ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) -> ( ( A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) with typecode |- |
44 |
43
|
3impib |
Could not format ( ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) with typecode |- |
45 |
2 3
|
dfgrlic2 |
|
46 |
45
|
3adant3 |
|
47 |
46
|
3ad2ant1 |
Could not format ( ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> ( G ~=lgr H <-> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> ( G ~=lgr H <-> E. f ( f : V -1-1-onto-> W /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( H ISubGr ( H ClNeighbVtx ( f ` x ) ) ) ) ) ) with typecode |- |
48 |
44 47
|
mpbird |
Could not format ( ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> G ~=lgr H ) : No typesetting found for |- ( ( ( G e. USGraph /\ H e. USGraph /\ V ~~ W ) /\ A. x e. V ( G ISubGr ( G ClNeighbVtx x ) ) ~=gr ( StarGr ` N ) /\ A. y e. W ( H ISubGr ( H ClNeighbVtx y ) ) ~=gr ( StarGr ` N ) ) -> G ~=lgr H ) with typecode |- |