Step |
Hyp |
Ref |
Expression |
1 |
|
pgpfi.1 |
|
2 |
|
eqid |
|
3 |
1 2
|
ispgp |
|
4 |
|
simprl |
|
5 |
1
|
grpbn0 |
|
6 |
5
|
ad2antrr |
|
7 |
|
hashnncl |
|
8 |
7
|
ad2antlr |
|
9 |
6 8
|
mpbird |
|
10 |
4 9
|
pccld |
|
11 |
10
|
nn0red |
|
12 |
11
|
leidd |
|
13 |
10
|
nn0zd |
|
14 |
|
pcid |
|
15 |
4 13 14
|
syl2anc |
|
16 |
12 15
|
breqtrrd |
|
17 |
16
|
ad2antrr |
|
18 |
|
simpr |
|
19 |
18
|
oveq1d |
|
20 |
18
|
oveq1d |
|
21 |
17 19 20
|
3brtr4d |
|
22 |
|
simp-4l |
|
23 |
|
simplr |
|
24 |
23
|
ad2antrr |
|
25 |
|
simplr |
|
26 |
|
simpr |
|
27 |
1 2
|
odcau |
|
28 |
22 24 25 26 27
|
syl31anc |
|
29 |
25
|
adantr |
|
30 |
|
prmz |
|
31 |
|
iddvds |
|
32 |
29 30 31
|
3syl |
|
33 |
|
simprr |
|
34 |
32 33
|
breqtrrd |
|
35 |
|
simplrr |
|
36 |
|
fveqeq2 |
|
37 |
36
|
rexbidv |
|
38 |
37
|
rspccva |
|
39 |
35 38
|
sylan |
|
40 |
39
|
ad2ant2r |
|
41 |
4
|
ad3antrrr |
|
42 |
|
prmnn |
|
43 |
29 42
|
syl |
|
44 |
33 43
|
eqeltrd |
|
45 |
|
pcprmpw |
|
46 |
41 44 45
|
syl2anc |
|
47 |
40 46
|
mpbid |
|
48 |
34 47
|
breqtrd |
|
49 |
41 44
|
pccld |
|
50 |
|
prmdvdsexpr |
|
51 |
29 41 49 50
|
syl3anc |
|
52 |
48 51
|
mpd |
|
53 |
28 52
|
rexlimddv |
|
54 |
53
|
ex |
|
55 |
54
|
necon3ad |
|
56 |
55
|
imp |
|
57 |
|
simplr |
|
58 |
9
|
ad2antrr |
|
59 |
|
pceq0 |
|
60 |
57 58 59
|
syl2anc |
|
61 |
56 60
|
mpbird |
|
62 |
|
prmnn |
|
63 |
62
|
ad2antrl |
|
64 |
63 10
|
nnexpcld |
|
65 |
64
|
ad2antrr |
|
66 |
57 65
|
pccld |
|
67 |
66
|
nn0ge0d |
|
68 |
61 67
|
eqbrtrd |
|
69 |
21 68
|
pm2.61dane |
|
70 |
69
|
ralrimiva |
|
71 |
|
hashcl |
|
72 |
71
|
ad2antlr |
|
73 |
72
|
nn0zd |
|
74 |
64
|
nnzd |
|
75 |
|
pc2dvds |
|
76 |
73 74 75
|
syl2anc |
|
77 |
70 76
|
mpbird |
|
78 |
|
oveq2 |
|
79 |
78
|
breq2d |
|
80 |
79
|
rspcev |
|
81 |
10 77 80
|
syl2anc |
|
82 |
|
pcprmpw2 |
|
83 |
|
pcprmpw |
|
84 |
82 83
|
bitr4d |
|
85 |
4 9 84
|
syl2anc |
|
86 |
81 85
|
mpbid |
|
87 |
4 86
|
jca |
|
88 |
87
|
3adantr2 |
|
89 |
88
|
ex |
|
90 |
3 89
|
syl5bi |
|
91 |
1
|
pgpfi1 |
|
92 |
91
|
3expia |
|
93 |
92
|
rexlimdv |
|
94 |
93
|
expimpd |
|
95 |
94
|
adantr |
|
96 |
90 95
|
impbid |
|