Step |
Hyp |
Ref |
Expression |
1 |
|
brric |
|
2 |
|
n0 |
|
3 |
1 2
|
bitri |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
4 5
|
rimf1o |
|
7 |
|
f1ofo |
|
8 |
|
foima |
|
9 |
6 7 8
|
3syl |
|
10 |
9
|
oveq2d |
|
11 |
|
rimrcl2 |
|
12 |
5
|
ressid |
|
13 |
11 12
|
syl |
|
14 |
10 13
|
eqtr2d |
|
15 |
14
|
adantr |
|
16 |
|
eqid |
|
17 |
|
eqid |
|
18 |
|
rimrhm |
|
19 |
18
|
adantr |
|
20 |
4
|
sdrgid |
|
21 |
20
|
adantl |
|
22 |
|
forn |
|
23 |
6 7 22
|
3syl |
|
24 |
23
|
adantr |
|
25 |
|
rhmrcl2 |
|
26 |
|
eqid |
|
27 |
5 26
|
ringidcl |
|
28 |
18 25 27
|
3syl |
|
29 |
|
eqid |
|
30 |
|
eqid |
|
31 |
29 30
|
drngunz |
|
32 |
31
|
adantl |
|
33 |
|
f1of1 |
|
34 |
6 33
|
syl |
|
35 |
|
drngring |
|
36 |
4 30
|
ringidcl |
|
37 |
35 36
|
syl |
|
38 |
4 29
|
ring0cl |
|
39 |
35 38
|
syl |
|
40 |
37 39
|
jca |
|
41 |
|
f1veqaeq |
|
42 |
34 40 41
|
syl2an |
|
43 |
42
|
imp |
|
44 |
32 43
|
mteqand |
|
45 |
30 26
|
rhm1 |
|
46 |
19 45
|
syl |
|
47 |
|
rhmghm |
|
48 |
29 17
|
ghmid |
|
49 |
19 47 48
|
3syl |
|
50 |
44 46 49
|
3netr3d |
|
51 |
|
nelsn |
|
52 |
50 51
|
syl |
|
53 |
|
nelne1 |
|
54 |
28 52 53
|
syl2an2r |
|
55 |
24 54
|
eqnetrd |
|
56 |
16 17 19 21 55
|
imadrhmcl |
|
57 |
15 56
|
eqeltrd |
|
58 |
57
|
ex |
|
59 |
58
|
exlimiv |
|
60 |
59
|
imp |
|
61 |
3 60
|
sylanb |
|