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
|
2idlelb |
|
10 |
9
|
simplbi |
|
11 |
10
|
ad2antlr |
|
12 |
6
|
lidlsubg |
|
13 |
5 11 12
|
syl2anc |
|
14 |
1 2
|
eqger |
|
15 |
13 14
|
syl |
|
16 |
|
simprl |
|
17 |
15 16
|
ersym |
|
18 |
|
ringabl |
|
19 |
18
|
ad2antrr |
|
20 |
1 3
|
2idlss |
|
21 |
20
|
ad2antlr |
|
22 |
|
eqid |
|
23 |
1 22 2
|
eqgabl |
|
24 |
19 21 23
|
syl2anc |
|
25 |
17 24
|
mpbid |
|
26 |
25
|
simp2d |
|
27 |
|
simprr |
|
28 |
1 22 2
|
eqgabl |
|
29 |
19 21 28
|
syl2anc |
|
30 |
27 29
|
mpbid |
|
31 |
30
|
simp1d |
|
32 |
1 4 5 26 31
|
ringcld |
|
33 |
25
|
simp1d |
|
34 |
30
|
simp2d |
|
35 |
1 4 5 33 34
|
ringcld |
|
36 |
|
ringgrp |
|
37 |
36
|
ad2antrr |
|
38 |
1 4 5 33 31
|
ringcld |
|
39 |
1 22
|
grpnnncan2 |
|
40 |
37 35 32 38 39
|
syl13anc |
|
41 |
1 4 22 5 33 34 31
|
ringsubdi |
|
42 |
30
|
simp3d |
|
43 |
6 1 4
|
lidlmcl |
|
44 |
5 11 33 42 43
|
syl22anc |
|
45 |
41 44
|
eqeltrrd |
|
46 |
|
eqid |
|
47 |
1 4 7 46
|
opprmul |
|
48 |
1 4 22 5 26 33 31
|
ringsubdir |
|
49 |
47 48
|
eqtrid |
|
50 |
7
|
opprring |
|
51 |
50
|
ad2antrr |
|
52 |
9
|
simprbi |
|
53 |
52
|
ad2antlr |
|
54 |
25
|
simp3d |
|
55 |
7 1
|
opprbas |
|
56 |
8 55 46
|
lidlmcl |
|
57 |
51 53 31 54 56
|
syl22anc |
|
58 |
49 57
|
eqeltrrd |
|
59 |
6 22
|
lidlsubcl |
|
60 |
5 11 45 58 59
|
syl22anc |
|
61 |
40 60
|
eqeltrrd |
|
62 |
1 22 2
|
eqgabl |
|
63 |
19 21 62
|
syl2anc |
|
64 |
32 35 61 63
|
mpbir3and |
|
65 |
64
|
ex |
|