Step |
Hyp |
Ref |
Expression |
1 |
|
ply1chr.1 |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
2 3 4
|
chrval |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
6 7 8
|
chrval |
|
10 |
9
|
eqcomi |
|
11 |
|
id |
|
12 |
11
|
crnggrpd |
|
13 |
|
crngring |
|
14 |
|
eqid |
|
15 |
14 7
|
ringidcl |
|
16 |
13 15
|
syl |
|
17 |
8
|
chrcl |
|
18 |
13 17
|
syl |
|
19 |
|
eqid |
|
20 |
|
eqid |
|
21 |
14 6 19 20
|
odeq |
|
22 |
12 16 18 21
|
syl3anc |
|
23 |
10 22
|
mpbii |
|
24 |
23
|
r19.21bi |
|
25 |
|
eqid |
|
26 |
13
|
adantr |
|
27 |
12
|
grpmndd |
|
28 |
27
|
adantr |
|
29 |
|
simpr |
|
30 |
16
|
adantr |
|
31 |
14 19
|
mulgnn0cl |
|
32 |
28 29 30 31
|
syl3anc |
|
33 |
|
simpl |
|
34 |
14 20
|
ring0cl |
|
35 |
33 13 34
|
3syl |
|
36 |
1 14 25 26 32 35
|
ply1scleq |
|
37 |
1
|
ply1sca |
|
38 |
37
|
adantr |
|
39 |
38
|
fveq2d |
|
40 |
39
|
oveqd |
|
41 |
40
|
fveq2d |
|
42 |
1
|
ply1assa |
|
43 |
42
|
adantr |
|
44 |
38
|
fveq2d |
|
45 |
30 44
|
eleqtrd |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
|
eqid |
|
49 |
|
eqid |
|
50 |
25 46 47 48 49
|
asclmulg |
|
51 |
43 29 45 50
|
syl3anc |
|
52 |
41 51
|
eqtrd |
|
53 |
|
eqid |
|
54 |
1 25 20 53
|
ply1scl0 |
|
55 |
33 13 54
|
3syl |
|
56 |
52 55
|
eqeq12d |
|
57 |
24 36 56
|
3bitr2d |
|
58 |
57
|
ralrimiva |
|
59 |
1
|
ply1crng |
|
60 |
59
|
crnggrpd |
|
61 |
|
eqid |
|
62 |
1 25 14 61
|
ply1sclcl |
|
63 |
13 16 62
|
syl2anc |
|
64 |
61 2 48 53
|
odeq |
|
65 |
60 63 18 64
|
syl3anc |
|
66 |
58 65
|
mpbird |
|
67 |
1 25 7 3
|
ply1scl1 |
|
68 |
67
|
fveq2d |
|
69 |
13 68
|
syl |
|
70 |
66 69
|
eqtr2d |
|
71 |
5 70
|
syl5eqr |
|