Step |
Hyp |
Ref |
Expression |
1 |
|
proot1hash.g |
|
2 |
|
proot1hash.o |
|
3 |
|
eqid |
|
4 |
3 2
|
odf |
|
5 |
|
ffn |
|
6 |
|
fniniseg2 |
|
7 |
4 5 6
|
mp2b |
|
8 |
|
simp3 |
|
9 |
|
fniniseg |
|
10 |
4 5 9
|
mp2b |
|
11 |
8 10
|
sylib |
|
12 |
11
|
simprd |
|
13 |
12
|
eqeq2d |
|
14 |
13
|
rabbidv |
|
15 |
|
isidom |
|
16 |
15
|
simprbi |
|
17 |
16
|
3ad2ant1 |
|
18 |
|
domnring |
|
19 |
|
eqid |
|
20 |
19 1
|
unitgrp |
|
21 |
17 18 20
|
3syl |
|
22 |
3
|
subgacs |
|
23 |
|
acsmre |
|
24 |
21 22 23
|
3syl |
|
25 |
|
eqid |
|
26 |
25
|
mrcssv |
|
27 |
|
dfrab3ss |
|
28 |
24 26 27
|
3syl |
|
29 |
|
incom |
|
30 |
|
simpl1 |
|
31 |
|
simpl2 |
|
32 |
|
simpr |
|
33 |
|
simpl3 |
|
34 |
1 2 25
|
proot1mul |
|
35 |
30 31 32 33 34
|
syl22anc |
|
36 |
35
|
ex |
|
37 |
36
|
ssrdv |
|
38 |
7 37
|
eqsstrrid |
|
39 |
|
df-ss |
|
40 |
38 39
|
sylib |
|
41 |
29 40
|
syl5eq |
|
42 |
14 28 41
|
3eqtrrd |
|
43 |
7 42
|
syl5eq |
|
44 |
43
|
fveq2d |
|
45 |
11
|
simpld |
|
46 |
|
simp2 |
|
47 |
12 46
|
eqeltrd |
|
48 |
3 2 25
|
odngen |
|
49 |
21 45 47 48
|
syl3anc |
|
50 |
12
|
fveq2d |
|
51 |
44 49 50
|
3eqtrd |
|