Step |
Hyp |
Ref |
Expression |
1 |
|
cusgrsizeindb0.v |
|
2 |
|
cusgrsizeindb0.e |
|
3 |
|
cusgrsizeinds.f |
|
4 |
1
|
fvexi |
|
5 |
|
hashnn0n0nn |
|
6 |
5
|
anassrs |
|
7 |
|
simplll |
|
8 |
|
simplr |
|
9 |
|
eleq1 |
|
10 |
9
|
eqcoms |
|
11 |
|
nnm1nn0 |
|
12 |
10 11
|
syl6bi |
|
13 |
12
|
ad2antlr |
|
14 |
13
|
imp |
|
15 |
|
nncn |
|
16 |
|
1cnd |
|
17 |
15 16
|
npcand |
|
18 |
17
|
eqcomd |
|
19 |
10 18
|
syl6bi |
|
20 |
19
|
ad2antlr |
|
21 |
20
|
imp |
|
22 |
|
hashdifsnp1 |
|
23 |
22
|
imp |
|
24 |
7 8 14 21 23
|
syl31anc |
|
25 |
|
oveq1 |
|
26 |
25
|
eqeq2d |
|
27 |
10
|
ad2antlr |
|
28 |
|
nnnn0 |
|
29 |
|
hashclb |
|
30 |
28 29
|
syl5ibrcom |
|
31 |
1 2 3
|
cusgrsizeinds |
|
32 |
|
oveq2 |
|
33 |
32
|
eqeq2d |
|
34 |
33
|
adantl |
|
35 |
|
bcn2m1 |
|
36 |
35
|
eqeq2d |
|
37 |
36
|
biimpd |
|
38 |
37
|
adantr |
|
39 |
34 38
|
sylbid |
|
40 |
39
|
ex |
|
41 |
40
|
com3r |
|
42 |
31 41
|
syl |
|
43 |
42
|
3exp |
|
44 |
43
|
com14 |
|
45 |
30 44
|
syldc |
|
46 |
45
|
com23 |
|
47 |
46
|
adantr |
|
48 |
47
|
imp |
|
49 |
27 48
|
sylbid |
|
50 |
49
|
imp |
|
51 |
50
|
com13 |
|
52 |
26 51
|
syl6bi |
|
53 |
52
|
com24 |
|
54 |
24 53
|
mpcom |
|
55 |
54
|
ex |
|
56 |
55
|
adantllr |
|
57 |
6 56
|
mpd |
|
58 |
57
|
exp41 |
|
59 |
58
|
com25 |
|
60 |
4 59
|
ax-mp |
|
61 |
60
|
3imp |
|
62 |
61
|
com12 |
|