Step |
Hyp |
Ref |
Expression |
1 |
|
smfliminflem.m |
|
2 |
|
smfliminflem.z |
|
3 |
|
smfliminflem.s |
|
4 |
|
smfliminflem.f |
|
5 |
|
smfliminflem.d |
|
6 |
|
smfliminflem.g |
|
7 |
6
|
a1i |
|
8 |
|
ssrab2 |
|
9 |
5 8
|
eqsstri |
|
10 |
|
id |
|
11 |
9 10
|
sseldi |
|
12 |
|
eqid |
|
13 |
2 12
|
allbutfi |
|
14 |
11 13
|
sylib |
|
15 |
14
|
adantl |
|
16 |
|
nfv |
|
17 |
|
nfra1 |
|
18 |
16 17
|
nfan |
|
19 |
2
|
fvexi |
|
20 |
19
|
a1i |
|
21 |
2
|
eluzelz2 |
|
22 |
21
|
zred |
|
23 |
22
|
ad2antlr |
|
24 |
|
simpll |
|
25 |
|
elinel1 |
|
26 |
3
|
adantr |
|
27 |
4
|
ffvelrnda |
|
28 |
|
eqid |
|
29 |
26 27 28
|
smff |
|
30 |
24 25 29
|
syl2an |
|
31 |
|
simplr |
|
32 |
|
eqid |
|
33 |
21
|
adantr |
|
34 |
2 25
|
eluzelz2d |
|
35 |
34
|
adantl |
|
36 |
22
|
rexrd |
|
37 |
36
|
adantr |
|
38 |
|
pnfxr |
|
39 |
38
|
a1i |
|
40 |
|
elinel2 |
|
41 |
40
|
adantl |
|
42 |
37 39 41
|
icogelbd |
|
43 |
32 33 35 42
|
eluzd |
|
44 |
43
|
adantlr |
|
45 |
|
rspa |
|
46 |
31 44 45
|
syl2anc |
|
47 |
46
|
adantlll |
|
48 |
30 47
|
ffvelrnd |
|
49 |
18 20 23 48
|
liminfval4 |
|
50 |
49
|
rexlimdva2 |
|
51 |
50
|
adantr |
|
52 |
15 51
|
mpd |
|
53 |
52
|
xnegeqd |
|
54 |
19
|
mptex |
|
55 |
54
|
limsupcli |
|
56 |
55
|
xnegnegi |
|
57 |
56
|
a1i |
|
58 |
53 57
|
eqtr2d |
|
59 |
5
|
rabeq2i |
|
60 |
59
|
simprbi |
|
61 |
60
|
adantl |
|
62 |
61
|
rexnegd |
|
63 |
58 62
|
eqtr2d |
|
64 |
61
|
renegcld |
|
65 |
63 64
|
eqeltrrd |
|
66 |
65
|
rexnegd |
|
67 |
52 66
|
eqtrd |
|
68 |
67
|
mpteq2dva |
|
69 |
7 68
|
eqtrd |
|
70 |
|
nfv |
|
71 |
21 32
|
uzn0d |
|
72 |
|
fvex |
|
73 |
72
|
dmex |
|
74 |
73
|
rgenw |
|
75 |
74
|
a1i |
|
76 |
|
iinexg |
|
77 |
71 75 76
|
syl2anc |
|
78 |
77
|
rgen |
|
79 |
|
iunexg |
|
80 |
19 78 79
|
mp2an |
|
81 |
80 9
|
ssexi |
|
82 |
81
|
a1i |
|
83 |
5
|
a1i |
|
84 |
13
|
biimpi |
|
85 |
50
|
imp |
|
86 |
84 85
|
sylan2 |
|
87 |
55
|
a1i |
|
88 |
|
simpl |
|
89 |
|
simpr |
|
90 |
88 89
|
eqeltrrd |
|
91 |
|
xnegrecl2 |
|
92 |
87 90 91
|
syl2anc |
|
93 |
|
simpl |
|
94 |
|
xnegrecl |
|
95 |
94
|
adantl |
|
96 |
93 95
|
eqeltrd |
|
97 |
92 96
|
impbida |
|
98 |
86 97
|
syl |
|
99 |
98
|
rabbidva |
|
100 |
83 99
|
eqtrd |
|
101 |
70 100
|
mpteq1df |
|
102 |
|
nfv |
|
103 |
|
nfv |
|
104 |
|
negex |
|
105 |
104
|
a1i |
|
106 |
|
nfv |
|
107 |
73
|
a1i |
|
108 |
29
|
ffvelrnda |
|
109 |
29
|
feqmptd |
|
110 |
109 27
|
eqeltrrd |
|
111 |
106 26 107 108 110
|
smfneg |
|
112 |
|
eqid |
|
113 |
|
eqid |
|
114 |
102 70 103 1 2 3 105 111 112 113
|
smflimsupmpt |
|
115 |
101 114
|
eqeltrd |
|
116 |
70 3 82 65 115
|
smfneg |
|
117 |
69 116
|
eqeltrd |
|