| Step |
Hyp |
Ref |
Expression |
| 1 |
|
elrgspn.b |
|
| 2 |
|
elrgspn.m |
|
| 3 |
|
elrgspn.x |
|
| 4 |
|
elrgspn.n |
|
| 5 |
|
elrgspn.f |
|
| 6 |
|
elrgspn.r |
|
| 7 |
|
elrgspn.a |
|
| 8 |
1
|
a1i |
|
| 9 |
4
|
a1i |
|
| 10 |
|
eqidd |
|
| 11 |
6 8 7 9 10
|
rgspncl |
|
| 12 |
1
|
subrgss |
|
| 13 |
11 12
|
syl |
|
| 14 |
13
|
sselda |
|
| 15 |
|
simpr |
|
| 16 |
|
eqid |
|
| 17 |
6
|
ringcmnd |
|
| 18 |
17
|
adantr |
|
| 19 |
1
|
fvexi |
|
| 20 |
19
|
a1i |
|
| 21 |
20 7
|
ssexd |
|
| 22 |
21
|
adantr |
|
| 23 |
|
wrdexg |
|
| 24 |
22 23
|
syl |
|
| 25 |
6
|
ringgrpd |
|
| 26 |
25
|
ad2antrr |
|
| 27 |
|
zex |
|
| 28 |
27
|
a1i |
|
| 29 |
|
breq1 |
|
| 30 |
29 5
|
elrab2 |
|
| 31 |
30
|
biimpi |
|
| 32 |
31
|
simpld |
|
| 33 |
32
|
adantl |
|
| 34 |
24 28 33
|
elmaprd |
|
| 35 |
34
|
ffvelcdmda |
|
| 36 |
2
|
ringmgp |
|
| 37 |
6 36
|
syl |
|
| 38 |
37
|
ad2antrr |
|
| 39 |
|
sswrd |
|
| 40 |
7 39
|
syl |
|
| 41 |
40
|
adantr |
|
| 42 |
41
|
sselda |
|
| 43 |
2 1
|
mgpbas |
|
| 44 |
43
|
gsumwcl |
|
| 45 |
38 42 44
|
syl2anc |
|
| 46 |
1 3 26 35 45
|
mulgcld |
|
| 47 |
46
|
fmpttd |
|
| 48 |
34
|
feqmptd |
|
| 49 |
31
|
simprd |
|
| 50 |
49
|
adantl |
|
| 51 |
48 50
|
eqbrtrrd |
|
| 52 |
1 16 3
|
mulg0 |
|
| 53 |
52
|
adantl |
|
| 54 |
|
fvexd |
|
| 55 |
51 53 35 45 54
|
fsuppssov1 |
|
| 56 |
1 16 18 24 47 55
|
gsumcl |
|
| 57 |
56
|
adantr |
|
| 58 |
15 57
|
eqeltrd |
|
| 59 |
58
|
r19.29an |
|
| 60 |
6
|
adantr |
|
| 61 |
7
|
adantr |
|
| 62 |
|
fveq1 |
|
| 63 |
62
|
oveq1d |
|
| 64 |
63
|
mpteq2dv |
|
| 65 |
|
fveq2 |
|
| 66 |
|
oveq2 |
|
| 67 |
65 66
|
oveq12d |
|
| 68 |
67
|
cbvmptv |
|
| 69 |
64 68
|
eqtrdi |
|
| 70 |
69
|
oveq2d |
|
| 71 |
70
|
cbvmptv |
|
| 72 |
71
|
rneqi |
|
| 73 |
1 2 3 4 5 60 61 72
|
elrgspnlem4 |
|
| 74 |
73
|
eleq2d |
|
| 75 |
|
fveq1 |
|
| 76 |
75
|
oveq1d |
|
| 77 |
76
|
mpteq2dv |
|
| 78 |
77
|
oveq2d |
|
| 79 |
78
|
cbvmptv |
|
| 80 |
79
|
elrnmpt |
|
| 81 |
80
|
adantl |
|
| 82 |
74 81
|
bitrd |
|
| 83 |
14 59 82
|
bibiad |
|