Step |
Hyp |
Ref |
Expression |
1 |
|
erclwwlkn.w |
|
2 |
|
erclwwlkn.r |
|
3 |
1 2
|
eclclwwlkn1 |
|
4 |
|
rabeq |
|
5 |
1 4
|
mp1i |
|
6 |
|
prmnn |
|
7 |
6
|
nnnn0d |
|
8 |
7
|
adantl |
|
9 |
1
|
eleq2i |
|
10 |
9
|
biimpi |
|
11 |
|
clwwlknscsh |
|
12 |
8 10 11
|
syl2an |
|
13 |
5 12
|
eqtrd |
|
14 |
13
|
eqeq2d |
|
15 |
6
|
adantl |
|
16 |
|
simpll |
|
17 |
|
elnnne0 |
|
18 |
|
eqeq1 |
|
19 |
18
|
eqcoms |
|
20 |
|
hasheq0 |
|
21 |
19 20
|
sylan9bbr |
|
22 |
21
|
necon3bid |
|
23 |
22
|
biimpcd |
|
24 |
17 23
|
simplbiim |
|
25 |
24
|
impcom |
|
26 |
|
simplr |
|
27 |
26
|
eqcomd |
|
28 |
16 25 27
|
3jca |
|
29 |
28
|
ex |
|
30 |
|
eqid |
|
31 |
30
|
clwwlknbp |
|
32 |
29 31
|
syl11 |
|
33 |
9 32
|
syl5bi |
|
34 |
15 33
|
syl |
|
35 |
34
|
imp |
|
36 |
|
scshwfzeqfzo |
|
37 |
35 36
|
syl |
|
38 |
37
|
eqeq2d |
|
39 |
|
fveq2 |
|
40 |
|
simprl |
|
41 |
|
prmuz2 |
|
42 |
41
|
adantl |
|
43 |
42
|
adantl |
|
44 |
|
simplr |
|
45 |
|
umgr2cwwkdifex |
|
46 |
40 43 44 45
|
syl3anc |
|
47 |
|
oveq2 |
|
48 |
47
|
eqeq2d |
|
49 |
48
|
cbvrexvw |
|
50 |
|
eqeq1 |
|
51 |
|
eqcom |
|
52 |
50 51
|
bitrdi |
|
53 |
52
|
rexbidv |
|
54 |
49 53
|
syl5bb |
|
55 |
54
|
cbvrabv |
|
56 |
55
|
cshwshashnsame |
|
57 |
56
|
ad2ant2rl |
|
58 |
46 57
|
mpd |
|
59 |
39 58
|
sylan9eqr |
|
60 |
59
|
exp41 |
|
61 |
60
|
adantr |
|
62 |
|
oveq1 |
|
63 |
62
|
eleq2d |
|
64 |
|
eleq1 |
|
65 |
64
|
anbi2d |
|
66 |
|
oveq2 |
|
67 |
66
|
rexeqdv |
|
68 |
67
|
rabbidv |
|
69 |
68
|
eqeq2d |
|
70 |
|
eqeq2 |
|
71 |
69 70
|
imbi12d |
|
72 |
65 71
|
imbi12d |
|
73 |
63 72
|
imbi12d |
|
74 |
73
|
eqcoms |
|
75 |
74
|
adantl |
|
76 |
61 75
|
mpbird |
|
77 |
31 76
|
mpcom |
|
78 |
77 1
|
eleq2s |
|
79 |
78
|
impcom |
|
80 |
38 79
|
sylbid |
|
81 |
14 80
|
sylbid |
|
82 |
81
|
rexlimdva |
|
83 |
82
|
com12 |
|
84 |
3 83
|
syl6bi |
|
85 |
84
|
pm2.43i |
|
86 |
85
|
com12 |
|