Step |
Hyp |
Ref |
Expression |
1 |
|
isdrngd.b |
|
2 |
|
isdrngd.t |
|
3 |
|
isdrngd.z |
|
4 |
|
isdrngd.u |
|
5 |
|
isdrngd.r |
|
6 |
|
isdrngd.n |
|
7 |
|
isdrngd.o |
|
8 |
|
isdrngd.i |
|
9 |
|
isdrngd.k |
|
10 |
|
difss |
|
11 |
10 1
|
sseqtrid |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
13 14
|
mgpbas |
|
16 |
12 15
|
ressbas2 |
|
17 |
11 16
|
syl |
|
18 |
|
fvex |
|
19 |
1 18
|
eqeltrdi |
|
20 |
|
difexg |
|
21 |
|
eqid |
|
22 |
13 21
|
mgpplusg |
|
23 |
12 22
|
ressplusg |
|
24 |
19 20 23
|
3syl |
|
25 |
2 24
|
eqtrd |
|
26 |
|
eldifsn |
|
27 |
|
eldifsn |
|
28 |
14 21
|
ringcl |
|
29 |
5 28
|
syl3an1 |
|
30 |
29
|
3expib |
|
31 |
1
|
eleq2d |
|
32 |
1
|
eleq2d |
|
33 |
31 32
|
anbi12d |
|
34 |
2
|
oveqd |
|
35 |
34 1
|
eleq12d |
|
36 |
30 33 35
|
3imtr4d |
|
37 |
36
|
3impib |
|
38 |
37
|
3adant2r |
|
39 |
38
|
3adant3r |
|
40 |
|
eldifsn |
|
41 |
39 6 40
|
sylanbrc |
|
42 |
27 41
|
syl3an3b |
|
43 |
26 42
|
syl3an2b |
|
44 |
14 21
|
ringass |
|
45 |
44
|
ex |
|
46 |
5 45
|
syl |
|
47 |
1
|
eleq2d |
|
48 |
31 32 47
|
3anbi123d |
|
49 |
|
eqidd |
|
50 |
2 34 49
|
oveq123d |
|
51 |
|
eqidd |
|
52 |
2
|
oveqd |
|
53 |
2 51 52
|
oveq123d |
|
54 |
50 53
|
eqeq12d |
|
55 |
46 48 54
|
3imtr4d |
|
56 |
|
eldifi |
|
57 |
|
eldifi |
|
58 |
|
eldifi |
|
59 |
56 57 58
|
3anim123i |
|
60 |
55 59
|
impel |
|
61 |
|
eqid |
|
62 |
14 61
|
ringidcl |
|
63 |
5 62
|
syl |
|
64 |
63 4 1
|
3eltr4d |
|
65 |
|
eldifsn |
|
66 |
64 7 65
|
sylanbrc |
|
67 |
14 21 61
|
ringlidm |
|
68 |
67
|
ex |
|
69 |
5 68
|
syl |
|
70 |
2 4 51
|
oveq123d |
|
71 |
70
|
eqeq1d |
|
72 |
69 31 71
|
3imtr4d |
|
73 |
72
|
imp |
|
74 |
73
|
adantrr |
|
75 |
26 74
|
sylan2b |
|
76 |
7
|
adantr |
|
77 |
|
simpr |
|
78 |
77
|
oveq1d |
|
79 |
9
|
adantr |
|
80 |
31
|
biimpa |
|
81 |
80
|
adantrr |
|
82 |
|
eqid |
|
83 |
14 21 82
|
ringlz |
|
84 |
5 81 83
|
syl2an2r |
|
85 |
2 3 51
|
oveq123d |
|
86 |
85
|
adantr |
|
87 |
3
|
adantr |
|
88 |
84 86 87
|
3eqtr4d |
|
89 |
88
|
adantr |
|
90 |
78 79 89
|
3eqtr3d |
|
91 |
76 90
|
mteqand |
|
92 |
|
eldifsn |
|
93 |
8 91 92
|
sylanbrc |
|
94 |
26 93
|
sylan2b |
|
95 |
26 9
|
sylan2b |
|
96 |
17 25 43 60 66 75 94 95
|
isgrpd |
|
97 |
3
|
sneqd |
|
98 |
1 97
|
difeq12d |
|
99 |
98
|
oveq2d |
|
100 |
99
|
eleq1d |
|
101 |
100
|
anbi2d |
|
102 |
5 96 101
|
mpbi2and |
|
103 |
|
eqid |
|
104 |
14 82 103
|
isdrng2 |
|
105 |
102 104
|
sylibr |
|