Step |
Hyp |
Ref |
Expression |
1 |
|
iunrelexpmin2.def |
|
2 |
|
simplr |
|
3 |
|
simpr |
|
4 |
3
|
oveq1d |
|
5 |
2 4
|
iuneq12d |
|
6 |
|
elex |
|
7 |
6
|
adantr |
|
8 |
|
nn0ex |
|
9 |
|
ovex |
|
10 |
8 9
|
iunex |
|
11 |
10
|
a1i |
|
12 |
1 5 7 11
|
fvmptd2 |
|
13 |
|
relexp0g |
|
14 |
13
|
sseq1d |
|
15 |
|
relexp1g |
|
16 |
15
|
sseq1d |
|
17 |
14 16
|
3anbi12d |
|
18 |
|
elnn0 |
|
19 |
|
oveq2 |
|
20 |
19
|
sseq1d |
|
21 |
20
|
imbi2d |
|
22 |
|
oveq2 |
|
23 |
22
|
sseq1d |
|
24 |
23
|
imbi2d |
|
25 |
|
oveq2 |
|
26 |
25
|
sseq1d |
|
27 |
26
|
imbi2d |
|
28 |
|
oveq2 |
|
29 |
28
|
sseq1d |
|
30 |
29
|
imbi2d |
|
31 |
|
simpr2 |
|
32 |
|
simp1 |
|
33 |
|
1nn |
|
34 |
33
|
a1i |
|
35 |
|
simp2l |
|
36 |
|
relexpaddnn |
|
37 |
32 34 35 36
|
syl3anc |
|
38 |
|
simp2r3 |
|
39 |
|
simp3 |
|
40 |
|
simp2r2 |
|
41 |
38 39 40
|
trrelssd |
|
42 |
37 41
|
eqsstrrd |
|
43 |
42
|
3exp |
|
44 |
43
|
a2d |
|
45 |
21 24 27 30 31 44
|
nnind |
|
46 |
|
simpr1 |
|
47 |
|
oveq2 |
|
48 |
47
|
sseq1d |
|
49 |
46 48
|
syl5ibr |
|
50 |
45 49
|
jaoi |
|
51 |
18 50
|
sylbi |
|
52 |
51
|
com12 |
|
53 |
52
|
ralrimiv |
|
54 |
|
iunss |
|
55 |
53 54
|
sylibr |
|
56 |
55
|
ex |
|
57 |
17 56
|
sylbird |
|
58 |
57
|
adantr |
|
59 |
|
sseq1 |
|
60 |
59
|
imbi2d |
|
61 |
58 60
|
syl5ibr |
|
62 |
12 61
|
mpcom |
|
63 |
62
|
alrimiv |
|