Step |
Hyp |
Ref |
Expression |
1 |
|
limsupre.1 |
|
2 |
|
limsupre.2 |
|
3 |
|
limsupre.f |
|
4 |
|
limsupre.bnd |
|
5 |
|
mnfxr |
|
6 |
5
|
a1i |
|
7 |
|
renegcl |
|
8 |
7
|
rexrd |
|
9 |
8
|
ad2antlr |
|
10 |
|
reex |
|
11 |
10
|
a1i |
|
12 |
11 1
|
ssexd |
|
13 |
|
fex |
|
14 |
3 12 13
|
syl2anc |
|
15 |
|
limsupcl |
|
16 |
14 15
|
syl |
|
17 |
16
|
ad2antrr |
|
18 |
7
|
mnfltd |
|
19 |
18
|
ad2antlr |
|
20 |
1
|
ad2antrr |
|
21 |
|
ressxr |
|
22 |
21
|
a1i |
|
23 |
3 22
|
fssd |
|
24 |
23
|
ad2antrr |
|
25 |
2
|
ad2antrr |
|
26 |
|
simpr |
|
27 |
|
nfv |
|
28 |
|
nfre1 |
|
29 |
27 28
|
nfan |
|
30 |
|
nfv |
|
31 |
|
nfv |
|
32 |
|
nfra1 |
|
33 |
30 31 32
|
nf3an |
|
34 |
|
simp13 |
|
35 |
|
simp2 |
|
36 |
|
simp3 |
|
37 |
|
rspa |
|
38 |
37
|
imp |
|
39 |
34 35 36 38
|
syl21anc |
|
40 |
|
simp11l |
|
41 |
3
|
ffvelrnda |
|
42 |
40 35 41
|
syl2anc |
|
43 |
|
simp11r |
|
44 |
42 43
|
absled |
|
45 |
39 44
|
mpbid |
|
46 |
45
|
simpld |
|
47 |
46
|
3exp |
|
48 |
33 47
|
ralrimi |
|
49 |
48
|
3exp |
|
50 |
49
|
adantr |
|
51 |
29 50
|
reximdai |
|
52 |
26 51
|
mpd |
|
53 |
|
breq2 |
|
54 |
|
fveq2 |
|
55 |
54
|
breq2d |
|
56 |
53 55
|
imbi12d |
|
57 |
56
|
cbvralvw |
|
58 |
|
breq1 |
|
59 |
58
|
imbi1d |
|
60 |
59
|
ralbidv |
|
61 |
57 60
|
syl5bb |
|
62 |
61
|
cbvrexvw |
|
63 |
52 62
|
sylibr |
|
64 |
20 24 9 25 63
|
limsupbnd2 |
|
65 |
6 9 17 19 64
|
xrltletrd |
|
66 |
65 4
|
r19.29a |
|
67 |
|
rexr |
|
68 |
67
|
ad2antlr |
|
69 |
|
pnfxr |
|
70 |
69
|
a1i |
|
71 |
45
|
simprd |
|
72 |
71
|
3exp |
|
73 |
33 72
|
ralrimi |
|
74 |
73
|
3exp |
|
75 |
74
|
adantr |
|
76 |
29 75
|
reximdai |
|
77 |
26 76
|
mpd |
|
78 |
54
|
breq1d |
|
79 |
53 78
|
imbi12d |
|
80 |
79
|
cbvralvw |
|
81 |
58
|
imbi1d |
|
82 |
81
|
ralbidv |
|
83 |
80 82
|
syl5bb |
|
84 |
83
|
cbvrexvw |
|
85 |
77 84
|
sylibr |
|
86 |
20 24 68 85
|
limsupbnd1 |
|
87 |
|
ltpnf |
|
88 |
87
|
ad2antlr |
|
89 |
17 68 70 86 88
|
xrlelttrd |
|
90 |
89 4
|
r19.29a |
|
91 |
|
xrrebnd |
|
92 |
16 91
|
syl |
|
93 |
66 90 92
|
mpbir2and |
|