Step |
Hyp |
Ref |
Expression |
1 |
|
smflimsuplem5.a |
|
2 |
|
smflimsuplem5.b |
|
3 |
|
smflimsuplem5.m |
|
4 |
|
smflimsuplem5.z |
|
5 |
|
smflimsuplem5.s |
|
6 |
|
smflimsuplem5.f |
|
7 |
|
smflimsuplem5.e |
|
8 |
|
smflimsuplem5.h |
|
9 |
|
smflimsuplem5.r |
|
10 |
|
smflimsuplem5.n |
|
11 |
|
smflimsuplem5.x |
|
12 |
4
|
eleq2i |
|
13 |
12
|
biimpi |
|
14 |
|
uzss |
|
15 |
13 14
|
syl |
|
16 |
15 4
|
sseqtrrdi |
|
17 |
10 16
|
syl |
|
18 |
17
|
sselda |
|
19 |
|
nfcv |
|
20 |
|
nfrab1 |
|
21 |
19 20
|
nfmpt |
|
22 |
7 21
|
nfcxfr |
|
23 |
|
nfcv |
|
24 |
22 23
|
nffv |
|
25 |
|
fvex |
|
26 |
24 25
|
mptexf |
|
27 |
26
|
a1i |
|
28 |
8
|
fvmpt2 |
|
29 |
18 27 28
|
syl2anc |
|
30 |
29
|
fveq1d |
|
31 |
|
nfcv |
|
32 |
|
nfcv |
|
33 |
|
nfcv |
|
34 |
|
fveq2 |
|
35 |
34
|
mpteq2dv |
|
36 |
35
|
rneqd |
|
37 |
36
|
supeq1d |
|
38 |
24 31 32 33 37
|
cbvmptf |
|
39 |
|
simpl |
|
40 |
39
|
fveq2d |
|
41 |
40
|
mpteq2dva |
|
42 |
41
|
rneqd |
|
43 |
42
|
supeq1d |
|
44 |
43
|
eleq1d |
|
45 |
|
uzss |
|
46 |
|
iinss1 |
|
47 |
45 46
|
syl |
|
48 |
47
|
adantl |
|
49 |
11
|
adantr |
|
50 |
48 49
|
sseldd |
|
51 |
|
nfv |
|
52 |
2 51
|
nfan |
|
53 |
|
eqid |
|
54 |
|
simpll |
|
55 |
45
|
sselda |
|
56 |
55
|
adantll |
|
57 |
5
|
adantr |
|
58 |
|
simpl |
|
59 |
17
|
sselda |
|
60 |
6
|
ffvelrnda |
|
61 |
58 59 60
|
syl2anc |
|
62 |
|
eqid |
|
63 |
57 61 62
|
smff |
|
64 |
|
eliin |
|
65 |
11 64
|
syl |
|
66 |
11 65
|
mpbid |
|
67 |
66
|
adantr |
|
68 |
|
simpr |
|
69 |
|
rspa |
|
70 |
67 68 69
|
syl2anc |
|
71 |
63 70
|
ffvelrnd |
|
72 |
54 56 71
|
syl2anc |
|
73 |
|
eluzelz |
|
74 |
73
|
adantl |
|
75 |
3
|
adantr |
|
76 |
|
fvex |
|
77 |
76
|
a1i |
|
78 |
52 74 75 53 4 72 77
|
limsupequzmpt |
|
79 |
9
|
adantr |
|
80 |
78 79
|
eqeltrd |
|
81 |
80
|
renepnfd |
|
82 |
52 53 72 81
|
limsupubuzmpt |
|
83 |
|
uzid2 |
|
84 |
83
|
ne0d |
|
85 |
84
|
adantl |
|
86 |
52 85 72
|
supxrre3rnmpt |
|
87 |
82 86
|
mpbird |
|
88 |
44 50 87
|
elrabd |
|
89 |
|
simpl |
|
90 |
89
|
fveq2d |
|
91 |
90
|
mpteq2dva |
|
92 |
91
|
rneqd |
|
93 |
92
|
supeq1d |
|
94 |
93
|
eleq1d |
|
95 |
94
|
cbvrabv |
|
96 |
88 95
|
eleqtrdi |
|
97 |
|
eqid |
|
98 |
|
fvex |
|
99 |
98
|
dmex |
|
100 |
99
|
rgenw |
|
101 |
100
|
a1i |
|
102 |
84 101
|
iinexd |
|
103 |
102
|
adantl |
|
104 |
97 103
|
rabexd |
|
105 |
7
|
fvmpt2 |
|
106 |
18 104 105
|
syl2anc |
|
107 |
96 106
|
eleqtrrd |
|
108 |
38 43 107 87
|
fvmptd3 |
|
109 |
30 108
|
eqtrd |
|
110 |
1 109
|
mpteq2da |
|
111 |
4
|
eluzelz2 |
|
112 |
10 111
|
syl |
|
113 |
|
eqid |
|
114 |
76
|
a1i |
|
115 |
76
|
a1i |
|
116 |
2 112 3 113 4 114 115
|
limsupequzmpt |
|
117 |
116 9
|
eqeltrd |
|
118 |
2 112 113 71 117
|
supcnvlimsupmpt |
|
119 |
110 118
|
eqbrtrd |
|