Step |
Hyp |
Ref |
Expression |
1 |
|
2idlcpbl.x |
|
2 |
|
2idlcpbl.r |
|
3 |
|
2idlcpbl.i |
|
4 |
|
2idlcpbl.t |
|
5 |
|
simpll |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
6 7 8 3
|
2idlval |
|
10 |
9
|
elin2 |
|
11 |
10
|
simplbi |
|
12 |
11
|
ad2antlr |
|
13 |
6
|
lidlsubg |
|
14 |
5 12 13
|
syl2anc |
|
15 |
1 2
|
eqger |
|
16 |
14 15
|
syl |
|
17 |
|
simprl |
|
18 |
16 17
|
ersym |
|
19 |
|
ringabl |
|
20 |
19
|
ad2antrr |
|
21 |
1 6
|
lidlss |
|
22 |
12 21
|
syl |
|
23 |
|
eqid |
|
24 |
1 23 2
|
eqgabl |
|
25 |
20 22 24
|
syl2anc |
|
26 |
18 25
|
mpbid |
|
27 |
26
|
simp2d |
|
28 |
|
simprr |
|
29 |
1 23 2
|
eqgabl |
|
30 |
20 22 29
|
syl2anc |
|
31 |
28 30
|
mpbid |
|
32 |
31
|
simp1d |
|
33 |
1 4
|
ringcl |
|
34 |
5 27 32 33
|
syl3anc |
|
35 |
26
|
simp1d |
|
36 |
31
|
simp2d |
|
37 |
1 4
|
ringcl |
|
38 |
5 35 36 37
|
syl3anc |
|
39 |
|
ringgrp |
|
40 |
39
|
ad2antrr |
|
41 |
1 4
|
ringcl |
|
42 |
5 35 32 41
|
syl3anc |
|
43 |
1 23
|
grpnnncan2 |
|
44 |
40 38 34 42 43
|
syl13anc |
|
45 |
1 4 23 5 35 36 32
|
ringsubdi |
|
46 |
31
|
simp3d |
|
47 |
6 1 4
|
lidlmcl |
|
48 |
5 12 35 46 47
|
syl22anc |
|
49 |
45 48
|
eqeltrrd |
|
50 |
|
eqid |
|
51 |
1 4 7 50
|
opprmul |
|
52 |
1 4 23 5 27 35 32
|
rngsubdir |
|
53 |
51 52
|
syl5eq |
|
54 |
7
|
opprring |
|
55 |
54
|
ad2antrr |
|
56 |
10
|
simprbi |
|
57 |
56
|
ad2antlr |
|
58 |
26
|
simp3d |
|
59 |
7 1
|
opprbas |
|
60 |
8 59 50
|
lidlmcl |
|
61 |
55 57 32 58 60
|
syl22anc |
|
62 |
53 61
|
eqeltrrd |
|
63 |
6 23
|
lidlsubcl |
|
64 |
5 12 49 62 63
|
syl22anc |
|
65 |
44 64
|
eqeltrrd |
|
66 |
1 23 2
|
eqgabl |
|
67 |
20 22 66
|
syl2anc |
|
68 |
34 38 65 67
|
mpbir3and |
|
69 |
68
|
ex |
|