Step |
Hyp |
Ref |
Expression |
1 |
|
deg1mhm.d |
|
2 |
|
deg1mhm.b |
|
3 |
|
deg1mhm.p |
|
4 |
|
deg1mhm.z |
|
5 |
|
deg1mhm.y |
|
6 |
|
deg1mhm.n |
|
7 |
3
|
ply1domn |
|
8 |
|
eqid |
|
9 |
2 4 8
|
isdomn3 |
|
10 |
9
|
simprbi |
|
11 |
7 10
|
syl |
|
12 |
5
|
submmnd |
|
13 |
11 12
|
syl |
|
14 |
|
nn0subm |
|
15 |
6
|
submmnd |
|
16 |
14 15
|
mp1i |
|
17 |
13 16
|
jca |
|
18 |
1 3 2
|
deg1xrf |
|
19 |
|
ffn |
|
20 |
18 19
|
ax-mp |
|
21 |
|
difss |
|
22 |
|
fnssres |
|
23 |
20 21 22
|
mp2an |
|
24 |
23
|
a1i |
|
25 |
|
fvres |
|
26 |
25
|
adantl |
|
27 |
|
domnring |
|
28 |
27
|
adantr |
|
29 |
|
eldifi |
|
30 |
29
|
adantl |
|
31 |
|
eldifsni |
|
32 |
31
|
adantl |
|
33 |
1 3 4 2
|
deg1nn0cl |
|
34 |
28 30 32 33
|
syl3anc |
|
35 |
26 34
|
eqeltrd |
|
36 |
35
|
ralrimiva |
|
37 |
|
ffnfv |
|
38 |
24 36 37
|
sylanbrc |
|
39 |
|
eqid |
|
40 |
|
eqid |
|
41 |
27
|
adantr |
|
42 |
29
|
ad2antrl |
|
43 |
31
|
ad2antrl |
|
44 |
|
simpl |
|
45 |
|
eqid |
|
46 |
1 3 4 2 39 45
|
deg1ldgdomn |
|
47 |
44 42 43 46
|
syl3anc |
|
48 |
|
eldifi |
|
49 |
48
|
ad2antll |
|
50 |
|
eldifsni |
|
51 |
50
|
ad2antll |
|
52 |
1 3 39 2 40 4 41 42 43 47 49 51
|
deg1mul2 |
|
53 |
|
domnring |
|
54 |
7 53
|
syl |
|
55 |
54
|
adantr |
|
56 |
2 40
|
ringcl |
|
57 |
55 42 49 56
|
syl3anc |
|
58 |
7
|
adantr |
|
59 |
2 40 4
|
domnmuln0 |
|
60 |
58 42 43 49 51 59
|
syl122anc |
|
61 |
|
eldifsn |
|
62 |
57 60 61
|
sylanbrc |
|
63 |
|
fvres |
|
64 |
62 63
|
syl |
|
65 |
|
fvres |
|
66 |
25 65
|
oveqan12d |
|
67 |
66
|
adantl |
|
68 |
52 64 67
|
3eqtr4d |
|
69 |
68
|
ralrimivva |
|
70 |
|
eqid |
|
71 |
2 70
|
ringidcl |
|
72 |
54 71
|
syl |
|
73 |
|
domnnzr |
|
74 |
70 4
|
nzrnz |
|
75 |
7 73 74
|
3syl |
|
76 |
|
eldifsn |
|
77 |
72 75 76
|
sylanbrc |
|
78 |
|
fvres |
|
79 |
77 78
|
syl |
|
80 |
8 70
|
ringidval |
|
81 |
5 80
|
subm0 |
|
82 |
11 81
|
syl |
|
83 |
82
|
fveq2d |
|
84 |
|
domnnzr |
|
85 |
|
eqid |
|
86 |
3 70 85 1
|
mon1pid |
|
87 |
86
|
simprd |
|
88 |
84 87
|
syl |
|
89 |
79 83 88
|
3eqtr3d |
|
90 |
38 69 89
|
3jca |
|
91 |
8 2
|
mgpbas |
|
92 |
5 91
|
ressbas2 |
|
93 |
21 92
|
ax-mp |
|
94 |
|
nn0sscn |
|
95 |
|
cnfldbas |
|
96 |
6 95
|
ressbas2 |
|
97 |
94 96
|
ax-mp |
|
98 |
2
|
fvexi |
|
99 |
|
difexg |
|
100 |
98 99
|
ax-mp |
|
101 |
8 40
|
mgpplusg |
|
102 |
5 101
|
ressplusg |
|
103 |
100 102
|
ax-mp |
|
104 |
|
nn0ex |
|
105 |
|
cnfldadd |
|
106 |
6 105
|
ressplusg |
|
107 |
104 106
|
ax-mp |
|
108 |
|
eqid |
|
109 |
|
cnfld0 |
|
110 |
6 109
|
subm0 |
|
111 |
14 110
|
ax-mp |
|
112 |
93 97 103 107 108 111
|
ismhm |
|
113 |
17 90 112
|
sylanbrc |
|