Step |
Hyp |
Ref |
Expression |
1 |
|
recn |
|
2 |
|
npcan1 |
|
3 |
2
|
eqcomd |
|
4 |
1 3
|
syl |
|
5 |
4
|
3ad2ant1 |
|
6 |
5
|
adantr |
|
7 |
6
|
oveq1d |
|
8 |
|
simpr |
|
9 |
|
1mod |
|
10 |
9
|
3adant1 |
|
11 |
10
|
adantr |
|
12 |
8 11
|
oveq12d |
|
13 |
12
|
oveq1d |
|
14 |
|
peano2rem |
|
15 |
14
|
3ad2ant1 |
|
16 |
|
1red |
|
17 |
|
simpl |
|
18 |
|
0lt1 |
|
19 |
|
0re |
|
20 |
|
1re |
|
21 |
|
lttr |
|
22 |
19 20 21
|
mp3an12 |
|
23 |
18 22
|
mpani |
|
24 |
23
|
imp |
|
25 |
17 24
|
elrpd |
|
26 |
25
|
3adant1 |
|
27 |
15 16 26
|
3jca |
|
28 |
27
|
adantr |
|
29 |
|
modaddabs |
|
30 |
28 29
|
syl |
|
31 |
|
0p1e1 |
|
32 |
31
|
oveq1i |
|
33 |
32 9
|
syl5eq |
|
34 |
33
|
3adant1 |
|
35 |
34
|
adantr |
|
36 |
13 30 35
|
3eqtr3d |
|
37 |
7 36
|
eqtrd |
|
38 |
|
simpr |
|
39 |
38
|
eqcomd |
|
40 |
39
|
oveq2d |
|
41 |
40
|
oveq1d |
|
42 |
|
simp1 |
|
43 |
42 26
|
modcld |
|
44 |
43
|
recnd |
|
45 |
44
|
subidd |
|
46 |
45
|
oveq1d |
|
47 |
|
modsubmod |
|
48 |
42 43 26 47
|
syl3anc |
|
49 |
|
0mod |
|
50 |
26 49
|
syl |
|
51 |
46 48 50
|
3eqtr3d |
|
52 |
51
|
adantr |
|
53 |
41 52
|
eqtrd |
|
54 |
37 53
|
impbida |
|