Step |
Hyp |
Ref |
Expression |
1 |
|
isupgr.v |
|
2 |
|
isupgr.e |
|
3 |
1 2
|
upgrn0 |
|
4 |
|
n0 |
|
5 |
3 4
|
sylib |
|
6 |
|
simp1 |
|
7 |
|
fndm |
|
8 |
7
|
eqcomd |
|
9 |
8
|
eleq2d |
|
10 |
9
|
biimpd |
|
11 |
10
|
a1i |
|
12 |
11
|
3imp |
|
13 |
1 2
|
upgrss |
|
14 |
6 12 13
|
syl2anc |
|
15 |
14
|
sselda |
|
16 |
15
|
adantr |
|
17 |
|
simpr |
|
18 |
|
ssdif0 |
|
19 |
17 18
|
sylibr |
|
20 |
|
simpr |
|
21 |
20
|
snssd |
|
22 |
21
|
adantr |
|
23 |
19 22
|
eqssd |
|
24 |
|
preq2 |
|
25 |
|
dfsn2 |
|
26 |
24 25
|
eqtr4di |
|
27 |
26
|
rspceeqv |
|
28 |
16 23 27
|
syl2anc |
|
29 |
|
n0 |
|
30 |
14
|
adantr |
|
31 |
|
simprr |
|
32 |
31
|
eldifad |
|
33 |
30 32
|
sseldd |
|
34 |
1 2
|
upgrfi |
|
35 |
34
|
adantr |
|
36 |
|
simprl |
|
37 |
36 32
|
prssd |
|
38 |
|
fvex |
|
39 |
|
ssdomg |
|
40 |
38 37 39
|
mpsyl |
|
41 |
1 2
|
upgrle |
|
42 |
41
|
adantr |
|
43 |
|
eldifsni |
|
44 |
43
|
ad2antll |
|
45 |
44
|
necomd |
|
46 |
|
hashprg |
|
47 |
46
|
el2v |
|
48 |
45 47
|
sylib |
|
49 |
42 48
|
breqtrrd |
|
50 |
|
prfi |
|
51 |
|
hashdom |
|
52 |
35 50 51
|
sylancl |
|
53 |
49 52
|
mpbid |
|
54 |
|
sbth |
|
55 |
40 53 54
|
syl2anc |
|
56 |
|
fisseneq |
|
57 |
35 37 55 56
|
syl3anc |
|
58 |
57
|
eqcomd |
|
59 |
33 58
|
jca |
|
60 |
59
|
expr |
|
61 |
60
|
eximdv |
|
62 |
61
|
imp |
|
63 |
|
df-rex |
|
64 |
62 63
|
sylibr |
|
65 |
29 64
|
sylan2b |
|
66 |
28 65
|
pm2.61dane |
|
67 |
15 66
|
jca |
|
68 |
67
|
ex |
|
69 |
68
|
eximdv |
|
70 |
5 69
|
mpd |
|
71 |
|
df-rex |
|
72 |
70 71
|
sylibr |
|