Step |
Hyp |
Ref |
Expression |
1 |
|
mptiunrelexp.def |
|
2 |
|
ovexd |
|
3 |
|
simprlr |
|
4 |
|
simpll2 |
|
5 |
3 4
|
eleqtrd |
|
6 |
|
simpll3 |
|
7 |
|
simprll |
|
8 |
7 4
|
eleqtrd |
|
9 |
|
eluznn0 |
|
10 |
6 8 9
|
syl2anc |
|
11 |
|
uzaddcl |
|
12 |
5 10 11
|
syl2anc |
|
13 |
|
simplr |
|
14 |
12 13 4
|
3eltr4d |
|
15 |
|
vex |
|
16 |
|
vex |
|
17 |
|
vex |
|
18 |
|
brcogw |
|
19 |
18
|
ex |
|
20 |
15 16 17 19
|
mp3an |
|
21 |
|
simpll3 |
|
22 |
|
simprr |
|
23 |
|
simpll2 |
|
24 |
22 23
|
eleqtrd |
|
25 |
|
eluznn0 |
|
26 |
21 24 25
|
syl2anc |
|
27 |
|
simprl |
|
28 |
27 23
|
eleqtrd |
|
29 |
21 28 9
|
syl2anc |
|
30 |
|
simpll1 |
|
31 |
|
relexpaddss |
|
32 |
26 29 30 31
|
syl3anc |
|
33 |
|
simplr |
|
34 |
33
|
oveq2d |
|
35 |
32 34
|
sseqtrrd |
|
36 |
35
|
ssbrd |
|
37 |
20 36
|
syl5 |
|
38 |
37
|
impr |
|
39 |
14 38
|
jca |
|
40 |
39
|
ex |
|
41 |
2 40
|
spcimedv |
|
42 |
41
|
exlimdvv |
|
43 |
|
reeanv |
|
44 |
|
r2ex |
|
45 |
43 44
|
bitr3i |
|
46 |
|
df-rex |
|
47 |
42 45 46
|
3imtr4g |
|
48 |
47
|
alrimiv |
|
49 |
48
|
alrimiv |
|
50 |
49
|
alrimiv |
|
51 |
|
cotr |
|
52 |
1
|
briunov2uz |
|
53 |
|
oveq2 |
|
54 |
53
|
breqd |
|
55 |
54
|
cbvrexvw |
|
56 |
52 55
|
syl6bb |
|
57 |
1
|
briunov2uz |
|
58 |
|
oveq2 |
|
59 |
58
|
breqd |
|
60 |
59
|
cbvrexvw |
|
61 |
57 60
|
syl6bb |
|
62 |
56 61
|
anbi12d |
|
63 |
1
|
briunov2uz |
|
64 |
62 63
|
imbi12d |
|
65 |
64
|
albidv |
|
66 |
65
|
albidv |
|
67 |
66
|
albidv |
|
68 |
51 67
|
syl5bb |
|
69 |
68
|
biimprd |
|
70 |
69
|
3adant3 |
|
71 |
50 70
|
mpd |
|