Step |
Hyp |
Ref |
Expression |
1 |
|
psgnghm.s |
|
2 |
|
psgnghm.n |
|
3 |
|
psgnghm.f |
|
4 |
|
psgnghm.u |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
1 5 6 2
|
psgnfn |
|
8 |
7
|
fndmi |
|
9 |
8
|
ssrab3 |
|
10 |
3 5
|
ressbas2 |
|
11 |
9 10
|
ax-mp |
|
12 |
4
|
cnmsgnbas |
|
13 |
11
|
fvexi |
|
14 |
|
eqid |
|
15 |
3 14
|
ressplusg |
|
16 |
13 15
|
ax-mp |
|
17 |
|
prex |
|
18 |
|
eqid |
|
19 |
|
cnfldmul |
|
20 |
18 19
|
mgpplusg |
|
21 |
4 20
|
ressplusg |
|
22 |
17 21
|
ax-mp |
|
23 |
1 2
|
psgndmsubg |
|
24 |
3
|
subggrp |
|
25 |
23 24
|
syl |
|
26 |
4
|
cnmsgngrp |
|
27 |
26
|
a1i |
|
28 |
|
fnfun |
|
29 |
7 28
|
ax-mp |
|
30 |
|
funfn |
|
31 |
29 30
|
mpbi |
|
32 |
31
|
a1i |
|
33 |
|
eqid |
|
34 |
1 33 2
|
psgnvali |
|
35 |
|
lencl |
|
36 |
35
|
nn0zd |
|
37 |
|
m1expcl2 |
|
38 |
|
prcom |
|
39 |
37 38
|
eleqtrdi |
|
40 |
|
eleq1a |
|
41 |
36 39 40
|
3syl |
|
42 |
41
|
adantld |
|
43 |
42
|
rexlimiv |
|
44 |
43
|
a1i |
|
45 |
34 44
|
syl5 |
|
46 |
45
|
ralrimiv |
|
47 |
|
ffnfv |
|
48 |
32 46 47
|
sylanbrc |
|
49 |
|
ccatcl |
|
50 |
1 33 2
|
psgnvalii |
|
51 |
49 50
|
sylan2 |
|
52 |
1
|
symggrp |
|
53 |
|
grpmnd |
|
54 |
52 53
|
syl |
|
55 |
33 1 5
|
symgtrf |
|
56 |
|
sswrd |
|
57 |
55 56
|
ax-mp |
|
58 |
57
|
sseli |
|
59 |
57
|
sseli |
|
60 |
5 14
|
gsumccat |
|
61 |
54 58 59 60
|
syl3an |
|
62 |
61
|
3expb |
|
63 |
62
|
fveq2d |
|
64 |
|
ccatlen |
|
65 |
64
|
adantl |
|
66 |
65
|
oveq2d |
|
67 |
|
neg1cn |
|
68 |
67
|
a1i |
|
69 |
|
lencl |
|
70 |
69
|
ad2antll |
|
71 |
35
|
ad2antrl |
|
72 |
68 70 71
|
expaddd |
|
73 |
66 72
|
eqtrd |
|
74 |
51 63 73
|
3eqtr3d |
|
75 |
|
oveq12 |
|
76 |
75
|
fveq2d |
|
77 |
|
oveq12 |
|
78 |
76 77
|
eqeqan12d |
|
79 |
78
|
an4s |
|
80 |
74 79
|
syl5ibrcom |
|
81 |
80
|
rexlimdvva |
|
82 |
1 33 2
|
psgnvali |
|
83 |
34 82
|
anim12i |
|
84 |
|
reeanv |
|
85 |
83 84
|
sylibr |
|
86 |
81 85
|
impel |
|
87 |
11 12 16 22 25 27 48 86
|
isghmd |
|