Step |
Hyp |
Ref |
Expression |
1 |
|
assapropd.1 |
|
2 |
|
assapropd.2 |
|
3 |
|
assapropd.3 |
|
4 |
|
assapropd.4 |
|
5 |
|
assapropd.5 |
|
6 |
|
assapropd.6 |
|
7 |
|
assapropd.7 |
|
8 |
|
assapropd.8 |
|
9 |
|
assalmod |
|
10 |
|
assaring |
|
11 |
9 10
|
jca |
|
12 |
11
|
a1i |
|
13 |
|
assalmod |
|
14 |
1 2 3 5 6 7 8
|
lmodpropd |
|
15 |
13 14
|
imbitrrid |
|
16 |
|
assaring |
|
17 |
1 2 3 4
|
ringpropd |
|
18 |
16 17
|
imbitrrid |
|
19 |
15 18
|
jcad |
|
20 |
14 17
|
anbi12d |
|
21 |
20
|
adantr |
|
22 |
|
simpll |
|
23 |
|
simplrl |
|
24 |
|
simprl |
|
25 |
5
|
fveq2d |
|
26 |
7 25
|
eqtrid |
|
27 |
22 26
|
syl |
|
28 |
24 27
|
eleqtrd |
|
29 |
|
simprrl |
|
30 |
22 1
|
syl |
|
31 |
29 30
|
eleqtrd |
|
32 |
|
eqid |
|
33 |
|
eqid |
|
34 |
|
eqid |
|
35 |
|
eqid |
|
36 |
32 33 34 35
|
lmodvscl |
|
37 |
23 28 31 36
|
syl3anc |
|
38 |
37 30
|
eleqtrrd |
|
39 |
|
simprrr |
|
40 |
4
|
oveqrspc2v |
|
41 |
22 38 39 40
|
syl12anc |
|
42 |
8
|
oveqrspc2v |
|
43 |
22 24 29 42
|
syl12anc |
|
44 |
43
|
oveq1d |
|
45 |
41 44
|
eqtrd |
|
46 |
|
eqid |
|
47 |
|
simplrr |
|
48 |
39 30
|
eleqtrd |
|
49 |
32 46 47 31 48
|
ringcld |
|
50 |
49 30
|
eleqtrrd |
|
51 |
8
|
oveqrspc2v |
|
52 |
22 24 50 51
|
syl12anc |
|
53 |
4
|
oveqrspc2v |
|
54 |
22 29 39 53
|
syl12anc |
|
55 |
54
|
oveq2d |
|
56 |
52 55
|
eqtrd |
|
57 |
45 56
|
eqeq12d |
|
58 |
32 33 34 35
|
lmodvscl |
|
59 |
23 28 48 58
|
syl3anc |
|
60 |
59 30
|
eleqtrrd |
|
61 |
4
|
oveqrspc2v |
|
62 |
22 29 60 61
|
syl12anc |
|
63 |
8
|
oveqrspc2v |
|
64 |
22 24 39 63
|
syl12anc |
|
65 |
64
|
oveq2d |
|
66 |
62 65
|
eqtrd |
|
67 |
66 56
|
eqeq12d |
|
68 |
57 67
|
anbi12d |
|
69 |
68
|
anassrs |
|
70 |
69
|
2ralbidva |
|
71 |
70
|
ralbidva |
|
72 |
26
|
adantr |
|
73 |
1
|
adantr |
|
74 |
73
|
raleqdv |
|
75 |
73 74
|
raleqbidv |
|
76 |
72 75
|
raleqbidv |
|
77 |
6
|
fveq2d |
|
78 |
7 77
|
eqtrid |
|
79 |
78
|
adantr |
|
80 |
2
|
adantr |
|
81 |
80
|
raleqdv |
|
82 |
80 81
|
raleqbidv |
|
83 |
79 82
|
raleqbidv |
|
84 |
71 76 83
|
3bitr3d |
|
85 |
21 84
|
anbi12d |
|
86 |
32 33 35 34 46
|
isassa |
|
87 |
|
eqid |
|
88 |
|
eqid |
|
89 |
|
eqid |
|
90 |
|
eqid |
|
91 |
|
eqid |
|
92 |
87 88 89 90 91
|
isassa |
|
93 |
85 86 92
|
3bitr4g |
|
94 |
93
|
ex |
|
95 |
12 19 94
|
pm5.21ndd |
|