Step |
Hyp |
Ref |
Expression |
1 |
|
infnsuprnmpt.x |
|
2 |
|
infnsuprnmpt.a |
|
3 |
|
infnsuprnmpt.b |
|
4 |
|
infnsuprnmpt.l |
|
5 |
|
eqid |
|
6 |
1 5 3
|
rnmptssd |
|
7 |
1 3 5 2
|
rnmptn0 |
|
8 |
4
|
rnmptlb |
|
9 |
|
infrenegsup |
|
10 |
6 7 8 9
|
syl3anc |
|
11 |
|
eqid |
|
12 |
|
rabidim2 |
|
13 |
12
|
adantl |
|
14 |
|
negex |
|
15 |
5
|
elrnmpt |
|
16 |
14 15
|
ax-mp |
|
17 |
13 16
|
sylib |
|
18 |
|
nfcv |
|
19 |
18
|
nfneg |
|
20 |
|
nfmpt1 |
|
21 |
20
|
nfrn |
|
22 |
19 21
|
nfel |
|
23 |
|
nfcv |
|
24 |
22 23
|
nfrabw |
|
25 |
18 24
|
nfel |
|
26 |
1 25
|
nfan |
|
27 |
|
rabidim1 |
|
28 |
27
|
adantl |
|
29 |
|
negeq |
|
30 |
29
|
eqcomd |
|
31 |
30
|
3ad2ant3 |
|
32 |
|
simp1r |
|
33 |
|
recn |
|
34 |
33
|
negnegd |
|
35 |
32 34
|
syl |
|
36 |
31 35
|
eqtr2d |
|
37 |
36
|
3exp |
|
38 |
28 37
|
syldan |
|
39 |
26 38
|
reximdai |
|
40 |
17 39
|
mpd |
|
41 |
|
simpr |
|
42 |
11 40 41
|
elrnmptd |
|
43 |
42
|
ex |
|
44 |
|
vex |
|
45 |
11
|
elrnmpt |
|
46 |
44 45
|
ax-mp |
|
47 |
46
|
biimpi |
|
48 |
47
|
adantl |
|
49 |
18 23
|
nfel |
|
50 |
49 22
|
nfan |
|
51 |
|
simp3 |
|
52 |
3
|
renegcld |
|
53 |
52
|
3adant3 |
|
54 |
51 53
|
eqeltrd |
|
55 |
|
simp2 |
|
56 |
51
|
negeqd |
|
57 |
3
|
recnd |
|
58 |
57
|
negnegd |
|
59 |
58
|
3adant3 |
|
60 |
56 59
|
eqtrd |
|
61 |
|
rspe |
|
62 |
55 60 61
|
syl2anc |
|
63 |
14
|
a1i |
|
64 |
5 62 63
|
elrnmptd |
|
65 |
54 64
|
jca |
|
66 |
65
|
3exp |
|
67 |
1 50 66
|
rexlimd |
|
68 |
67
|
imp |
|
69 |
48 68
|
syldan |
|
70 |
|
rabid |
|
71 |
69 70
|
sylibr |
|
72 |
71
|
ex |
|
73 |
43 72
|
impbid |
|
74 |
73
|
alrimiv |
|
75 |
|
nfrab1 |
|
76 |
|
nfcv |
|
77 |
75 76
|
cleqf |
|
78 |
74 77
|
sylibr |
|
79 |
78
|
supeq1d |
|
80 |
79
|
negeqd |
|
81 |
|
eqidd |
|
82 |
10 80 81
|
3eqtrd |
|