Step |
Hyp |
Ref |
Expression |
1 |
|
elnn0 |
|
2 |
|
oveq2 |
|
3 |
2
|
cnveqd |
|
4 |
|
oveq2 |
|
5 |
3 4
|
eqeq12d |
|
6 |
5
|
imbi2d |
|
7 |
|
oveq2 |
|
8 |
7
|
cnveqd |
|
9 |
|
oveq2 |
|
10 |
8 9
|
eqeq12d |
|
11 |
10
|
imbi2d |
|
12 |
|
oveq2 |
|
13 |
12
|
cnveqd |
|
14 |
|
oveq2 |
|
15 |
13 14
|
eqeq12d |
|
16 |
15
|
imbi2d |
|
17 |
|
oveq2 |
|
18 |
17
|
cnveqd |
|
19 |
|
oveq2 |
|
20 |
18 19
|
eqeq12d |
|
21 |
20
|
imbi2d |
|
22 |
|
relexp1g |
|
23 |
22
|
cnveqd |
|
24 |
|
cnvexg |
|
25 |
|
relexp1g |
|
26 |
24 25
|
syl |
|
27 |
23 26
|
eqtr4d |
|
28 |
|
cnvco |
|
29 |
|
simp3 |
|
30 |
29
|
coeq2d |
|
31 |
28 30
|
syl5eq |
|
32 |
|
simp2 |
|
33 |
|
simp1 |
|
34 |
|
relexpsucnnr |
|
35 |
32 33 34
|
syl2anc |
|
36 |
35
|
cnveqd |
|
37 |
32 24
|
syl |
|
38 |
|
relexpsucnnl |
|
39 |
37 33 38
|
syl2anc |
|
40 |
31 36 39
|
3eqtr4d |
|
41 |
40
|
3exp |
|
42 |
41
|
a2d |
|
43 |
6 11 16 21 27 42
|
nnind |
|
44 |
|
cnvresid |
|
45 |
|
uncom |
|
46 |
|
df-rn |
|
47 |
|
dfdm4 |
|
48 |
46 47
|
uneq12i |
|
49 |
45 48
|
eqtri |
|
50 |
49
|
reseq2i |
|
51 |
44 50
|
eqtri |
|
52 |
|
oveq2 |
|
53 |
|
relexp0g |
|
54 |
52 53
|
sylan9eq |
|
55 |
54
|
cnveqd |
|
56 |
|
oveq2 |
|
57 |
56
|
adantr |
|
58 |
|
simpr |
|
59 |
|
relexp0g |
|
60 |
58 24 59
|
3syl |
|
61 |
57 60
|
eqtrd |
|
62 |
51 55 61
|
3eqtr4a |
|
63 |
62
|
ex |
|
64 |
43 63
|
jaoi |
|
65 |
1 64
|
sylbi |
|
66 |
65
|
imp |
|