Step | Hyp | Ref
| Expression |
1 | | nndi 6088 |
. . . . . . . 8
|
2 | 1 | adantl 271 |
. . . . . . 7
|
3 | | simplll 499 |
. . . . . . . 8
|
4 | | simprlr 504 |
. . . . . . . . 9
|
5 | | pinn 6499 |
. . . . . . . . 9
|
6 | 4, 5 | syl 14 |
. . . . . . . 8
|
7 | | nnmcl 6083 |
. . . . . . . 8
|
8 | 3, 6, 7 | syl2anc 403 |
. . . . . . 7
|
9 | | simpllr 500 |
. . . . . . . . 9
|
10 | | pinn 6499 |
. . . . . . . . 9
|
11 | 9, 10 | syl 14 |
. . . . . . . 8
|
12 | | simprll 503 |
. . . . . . . 8
|
13 | | nnmcl 6083 |
. . . . . . . 8
|
14 | 11, 12, 13 | syl2anc 403 |
. . . . . . 7
|
15 | | simplrr 502 |
. . . . . . . . 9
|
16 | | pinn 6499 |
. . . . . . . . 9
|
17 | 15, 16 | syl 14 |
. . . . . . . 8
|
18 | | simprrr 506 |
. . . . . . . . 9
|
19 | | pinn 6499 |
. . . . . . . . 9
|
20 | 18, 19 | syl 14 |
. . . . . . . 8
|
21 | | nnmcl 6083 |
. . . . . . . 8
|
22 | 17, 20, 21 | syl2anc 403 |
. . . . . . 7
|
23 | | nnacl 6082 |
. . . . . . . 8
|
24 | 23 | adantl 271 |
. . . . . . 7
|
25 | | nnmcom 6091 |
. . . . . . . 8
|
26 | 25 | adantl 271 |
. . . . . . 7
|
27 | 2, 8, 14, 22, 24, 26 | caovdir2d 5697 |
. . . . . 6
|
28 | | nnmass 6089 |
. . . . . . . . 9
|
29 | 28 | adantl 271 |
. . . . . . . 8
|
30 | | nnmcl 6083 |
. . . . . . . . 9
|
31 | 30 | adantl 271 |
. . . . . . . 8
|
32 | 3, 6, 17, 26, 29, 20, 31 | caov4d 5705 |
. . . . . . 7
|
33 | 11, 12, 17, 26, 29, 20, 31 | caov4d 5705 |
. . . . . . 7
|
34 | 32, 33 | oveq12d 5550 |
. . . . . 6
|
35 | 27, 34 | eqtrd 2113 |
. . . . 5
|
36 | | oveq1 5539 |
. . . . . 6
|
37 | | oveq2 5540 |
. . . . . 6
|
38 | 36, 37 | oveqan12d 5551 |
. . . . 5
|
39 | 35, 38 | sylan9eq 2133 |
. . . 4
|
40 | | nnmcl 6083 |
. . . . . . . 8
|
41 | 11, 6, 40 | syl2anc 403 |
. . . . . . 7
|
42 | | simplrl 501 |
. . . . . . . 8
|
43 | | nnmcl 6083 |
. . . . . . . 8
|
44 | 42, 20, 43 | syl2anc 403 |
. . . . . . 7
|
45 | | simprrl 505 |
. . . . . . . 8
|
46 | | nnmcl 6083 |
. . . . . . . 8
|
47 | 17, 45, 46 | syl2anc 403 |
. . . . . . 7
|
48 | | nndi 6088 |
. . . . . . 7
|
49 | 41, 44, 47, 48 | syl3anc 1169 |
. . . . . 6
|
50 | 11, 6, 42, 26, 29, 20, 31 | caov4d 5705 |
. . . . . . 7
|
51 | 11, 6, 17, 26, 29, 45, 31 | caov4d 5705 |
. . . . . . 7
|
52 | 50, 51 | oveq12d 5550 |
. . . . . 6
|
53 | 49, 52 | eqtrd 2113 |
. . . . 5
|
54 | 53 | adantr 270 |
. . . 4
|
55 | 39, 54 | eqtr4d 2116 |
. . 3
|
56 | | nnacl 6082 |
. . . . . 6
|
57 | 8, 14, 56 | syl2anc 403 |
. . . . 5
|
58 | | mulpiord 6507 |
. . . . . . . 8
|
59 | | mulclpi 6518 |
. . . . . . . 8
|
60 | 58, 59 | eqeltrrd 2156 |
. . . . . . 7
|
61 | 60 | ad2ant2l 491 |
. . . . . 6
|
62 | 61 | ad2ant2r 492 |
. . . . 5
|
63 | | nnacl 6082 |
. . . . . 6
|
64 | 44, 47, 63 | syl2anc 403 |
. . . . 5
|
65 | | mulpiord 6507 |
. . . . . . . 8
|
66 | | mulclpi 6518 |
. . . . . . . 8
|
67 | 65, 66 | eqeltrrd 2156 |
. . . . . . 7
|
68 | 67 | ad2ant2l 491 |
. . . . . 6
|
69 | 68 | ad2ant2l 491 |
. . . . 5
|
70 | | enq0breq 6626 |
. . . . 5
~Q0
|
71 | 57, 62, 64, 69, 70 | syl22anc 1170 |
. . . 4
~Q0
|
72 | 71 | adantr 270 |
. . 3
~Q0
|
73 | 55, 72 | mpbird 165 |
. 2
~Q0 |
74 | 73 | ex 113 |
1
~Q0 |