Step |
Hyp |
Ref |
Expression |
1 |
|
mplcoe1.p |
|
2 |
|
mplcoe1.d |
|
3 |
|
mplcoe1.z |
|
4 |
|
mplcoe1.o |
|
5 |
|
mplcoe1.i |
|
6 |
|
mplcoe2.g |
|
7 |
|
mplcoe2.m |
|
8 |
|
mplcoe2.v |
|
9 |
|
mplcoe5.r |
|
10 |
|
mplcoe5.y |
|
11 |
|
mplcoe5.c |
|
12 |
|
mplcoe5.s |
|
13 |
|
vex |
|
14 |
|
eqid |
|
15 |
14
|
elrnmpt |
|
16 |
13 15
|
mp1i |
|
17 |
|
vex |
|
18 |
14
|
elrnmpt |
|
19 |
17 18
|
mp1i |
|
20 |
|
fveq2 |
|
21 |
|
fveq2 |
|
22 |
20 21
|
oveq12d |
|
23 |
22
|
eqeq2d |
|
24 |
23
|
cbvrexvw |
|
25 |
|
eqid |
|
26 |
|
eqid |
|
27 |
6 26
|
mgpplusg |
|
28 |
27
|
eqcomi |
|
29 |
1
|
mplring |
|
30 |
5 9 29
|
syl2anc |
|
31 |
|
ringsrg |
|
32 |
30 31
|
syl |
|
33 |
32
|
adantr |
|
34 |
33
|
adantr |
|
35 |
6 25
|
mgpbas |
|
36 |
6
|
ringmgp |
|
37 |
30 36
|
syl |
|
38 |
37
|
adantr |
|
39 |
12
|
sseld |
|
40 |
39
|
imdistani |
|
41 |
2
|
psrbag |
|
42 |
5 41
|
syl |
|
43 |
10 42
|
mpbid |
|
44 |
43
|
simpld |
|
45 |
44
|
ffvelcdmda |
|
46 |
40 45
|
syl |
|
47 |
5
|
adantr |
|
48 |
9
|
adantr |
|
49 |
12
|
sselda |
|
50 |
1 8 25 47 48 49
|
mvrcl |
|
51 |
35 7 38 46 50
|
mulgnn0cld |
|
52 |
51
|
adantr |
|
53 |
5
|
adantr |
|
54 |
9
|
adantr |
|
55 |
12
|
sselda |
|
56 |
1 8 25 53 54 55
|
mvrcl |
|
57 |
56
|
adantlr |
|
58 |
44
|
ffvelcdmda |
|
59 |
55 58
|
syldan |
|
60 |
59
|
adantlr |
|
61 |
50
|
adantr |
|
62 |
46
|
adantr |
|
63 |
|
fveq2 |
|
64 |
63
|
oveq2d |
|
65 |
63
|
oveq1d |
|
66 |
64 65
|
eqeq12d |
|
67 |
|
fveq2 |
|
68 |
67
|
oveq1d |
|
69 |
67
|
oveq2d |
|
70 |
68 69
|
eqeq12d |
|
71 |
66 70
|
rspc2v |
|
72 |
49 55
|
anim12dan |
|
73 |
71 72
|
syl11 |
|
74 |
73
|
expd |
|
75 |
11 74
|
mpcom |
|
76 |
75
|
impl |
|
77 |
25 28 6 7 34 57 61 62 76
|
srgpcomp |
|
78 |
25 28 6 7 34 52 57 60 77
|
srgpcomp |
|
79 |
|
oveq12 |
|
80 |
|
oveq12 |
|
81 |
80
|
ancoms |
|
82 |
79 81
|
eqeq12d |
|
83 |
78 82
|
syl5ibrcom |
|
84 |
83
|
expd |
|
85 |
84
|
rexlimdva |
|
86 |
85
|
com23 |
|
87 |
86
|
rexlimdva |
|
88 |
24 87
|
biimtrid |
|
89 |
19 88
|
sylbid |
|
90 |
89
|
com23 |
|
91 |
16 90
|
sylbid |
|
92 |
91
|
imp32 |
|
93 |
92
|
ralrimivva |
|
94 |
|
eqid |
|
95 |
37
|
adantr |
|
96 |
12
|
sseld |
|
97 |
96
|
imdistani |
|
98 |
97 58
|
syl |
|
99 |
56 35
|
eleqtrdi |
|
100 |
94 7 95 98 99
|
mulgnn0cld |
|
101 |
100
|
fmpttd |
|
102 |
101
|
frnd |
|
103 |
|
eqid |
|
104 |
|
eqid |
|
105 |
94 103 104
|
sscntz |
|
106 |
102 102 105
|
syl2anc |
|
107 |
93 106
|
mpbird |
|