Step |
Hyp |
Ref |
Expression |
1 |
|
decex |
|
2 |
|
eleq1 |
|
3 |
|
oveq2 |
|
4 |
|
id |
|
5 |
3 4
|
oveq12d |
|
6 |
|
oveq2 |
|
7 |
5 6
|
eqeq12d |
|
8 |
|
eleq1 |
|
9 |
7 8
|
imbi12d |
|
10 |
9
|
notbid |
|
11 |
2 10
|
anbi12d |
|
12 |
|
3z |
|
13 |
|
3nn0 |
|
14 |
|
4nn0 |
|
15 |
13 14
|
deccl |
|
16 |
|
1nn0 |
|
17 |
15 16
|
deccl |
|
18 |
17
|
nn0zi |
|
19 |
13
|
dec0h |
|
20 |
|
0nn0 |
|
21 |
|
3re |
|
22 |
|
9re |
|
23 |
|
3lt9 |
|
24 |
21 22 23
|
ltleii |
|
25 |
|
3nn |
|
26 |
|
0re |
|
27 |
|
9pos |
|
28 |
26 22 27
|
ltleii |
|
29 |
25 14 20 28
|
decltdi |
|
30 |
20 15 13 16 24 29
|
decleh |
|
31 |
19 30
|
eqbrtri |
|
32 |
|
eluz2 |
|
33 |
12 18 31 32
|
mpbir3an |
|
34 |
|
341fppr2 |
|
35 |
|
fpprwppr |
|
36 |
34 35
|
ax-mp |
|
37 |
|
11t31e341 |
|
38 |
37
|
eqcomi |
|
39 |
|
2z |
|
40 |
16 16
|
deccl |
|
41 |
40
|
nn0zi |
|
42 |
|
2nn0 |
|
43 |
42
|
dec0h |
|
44 |
|
2re |
|
45 |
|
2lt9 |
|
46 |
44 22 45
|
ltleii |
|
47 |
|
0lt1 |
|
48 |
20 16 42 16 46 47
|
decleh |
|
49 |
43 48
|
eqbrtri |
|
50 |
|
eluz2 |
|
51 |
39 41 49 50
|
mpbir3an |
|
52 |
13 16
|
deccl |
|
53 |
52
|
nn0zi |
|
54 |
|
3pos |
|
55 |
20 13 42 16 46 54
|
decleh |
|
56 |
43 55
|
eqbrtri |
|
57 |
|
eluz2 |
|
58 |
39 53 56 57
|
mpbir3an |
|
59 |
|
nprm |
|
60 |
51 58 59
|
mp2an |
|
61 |
38 60
|
eqneltri |
|
62 |
36 61
|
pm3.2i |
|
63 |
|
annim |
|
64 |
62 63
|
mpbi |
|
65 |
33 64
|
pm3.2i |
|
66 |
1 11 65
|
ceqsexv2d |
|
67 |
|
df-rex |
|
68 |
66 67
|
mpbir |
|