Step |
Hyp |
Ref |
Expression |
1 |
|
hashcl |
|
2 |
1
|
adantl |
|
3 |
|
eqid |
|
4 |
3
|
zncrng |
|
5 |
|
crngring |
|
6 |
|
ringabl |
|
7 |
2 4 5 6
|
4syl |
|
8 |
|
hashnncl |
|
9 |
8
|
biimparc |
|
10 |
|
eqid |
|
11 |
3 10
|
znhash |
|
12 |
9 11
|
syl |
|
13 |
12
|
eqcomd |
|
14 |
|
simpr |
|
15 |
3 10
|
znfi |
|
16 |
9 15
|
syl |
|
17 |
|
hashen |
|
18 |
14 16 17
|
syl2anc |
|
19 |
13 18
|
mpbid |
|
20 |
10
|
isnumbasgrplem1 |
|
21 |
7 19 20
|
syl2anc |
|
22 |
21
|
adantll |
|
23 |
|
2nn0 |
|
24 |
|
eqid |
|
25 |
24
|
zncrng |
|
26 |
|
crngring |
|
27 |
23 25 26
|
mp2b |
|
28 |
|
eqid |
|
29 |
28
|
frlmlmod |
|
30 |
27 29
|
mpan |
|
31 |
|
lmodabl |
|
32 |
30 31
|
syl |
|
33 |
32
|
ad2antrr |
|
34 |
|
eqid |
|
35 |
24 28 34
|
frlmpwfi |
|
36 |
35
|
ad2antrr |
|
37 |
|
simpll |
|
38 |
|
numinfctb |
|
39 |
38
|
adantlr |
|
40 |
|
infpwfien |
|
41 |
37 39 40
|
syl2anc |
|
42 |
|
entr |
|
43 |
36 41 42
|
syl2anc |
|
44 |
43
|
ensymd |
|
45 |
34
|
isnumbasgrplem1 |
|
46 |
33 44 45
|
syl2anc |
|
47 |
22 46
|
pm2.61dan |
|