Step |
Hyp |
Ref |
Expression |
1 |
|
smfliminfmpt.p |
|
2 |
|
smfliminfmpt.x |
|
3 |
|
smfliminfmpt.n |
|
4 |
|
smfliminfmpt.m |
|
5 |
|
smfliminfmpt.z |
|
6 |
|
smfliminfmpt.s |
|
7 |
|
smfliminfmpt.b |
|
8 |
|
smfliminfmpt.f |
|
9 |
|
smfliminfmpt.d |
|
10 |
|
smfliminfmpt.g |
|
11 |
10
|
a1i |
|
12 |
9
|
a1i |
|
13 |
|
simpr |
|
14 |
|
nfv |
|
15 |
1 14
|
nfan |
|
16 |
|
simpll |
|
17 |
5
|
uztrn2 |
|
18 |
17
|
adantll |
|
19 |
|
simpr |
|
20 |
8
|
elexd |
|
21 |
|
eqid |
|
22 |
21
|
fvmpt2 |
|
23 |
19 20 22
|
syl2anc |
|
24 |
23
|
dmeqd |
|
25 |
|
nfv |
|
26 |
2 25
|
nfan |
|
27 |
|
eqid |
|
28 |
7
|
3expa |
|
29 |
26 27 28
|
dmmptdf |
|
30 |
24 29
|
eqtr2d |
|
31 |
16 18 30
|
syl2anc |
|
32 |
15 31
|
iineq2d |
|
33 |
3 32
|
iuneq2df |
|
34 |
33
|
adantr |
|
35 |
13 34
|
eleqtrd |
|
36 |
35
|
adantrr |
|
37 |
|
eliun |
|
38 |
37
|
biimpi |
|
39 |
38
|
adantl |
|
40 |
|
nfv |
|
41 |
|
nfcv |
|
42 |
|
nfii1 |
|
43 |
41 42
|
nfel |
|
44 |
1 14 43
|
nf3an |
|
45 |
23
|
fveq1d |
|
46 |
16 18 45
|
syl2anc |
|
47 |
46
|
3adantl3 |
|
48 |
|
eliinid |
|
49 |
48
|
3ad2antl3 |
|
50 |
|
simpl1 |
|
51 |
|
simp2 |
|
52 |
51 17
|
sylan |
|
53 |
50 52 49 7
|
syl3anc |
|
54 |
27
|
fvmpt2 |
|
55 |
49 53 54
|
syl2anc |
|
56 |
47 55
|
eqtrd |
|
57 |
44 56
|
mpteq2da |
|
58 |
57
|
fveq2d |
|
59 |
|
nfcv |
|
60 |
|
nfcv |
|
61 |
|
eqid |
|
62 |
5
|
eluzelz2 |
|
63 |
62
|
uzidd |
|
64 |
63
|
3ad2ant2 |
|
65 |
|
fvexd |
|
66 |
44 59 60 5 61 51 64 65
|
liminfequzmpt2 |
|
67 |
44 59 60 5 61 51 64 53
|
liminfequzmpt2 |
|
68 |
58 66 67
|
3eqtr4d |
|
69 |
68
|
3exp |
|
70 |
3 40 69
|
rexlimd |
|
71 |
70
|
adantr |
|
72 |
39 71
|
mpd |
|
73 |
72
|
adantrr |
|
74 |
|
simprr |
|
75 |
73 74
|
eqeltrd |
|
76 |
36 75
|
jca |
|
77 |
|
simpl |
|
78 |
|
simpr |
|
79 |
33
|
eqcomd |
|
80 |
79
|
adantr |
|
81 |
78 80
|
eleqtrd |
|
82 |
81
|
adantrr |
|
83 |
|
simprr |
|
84 |
|
simp2 |
|
85 |
72
|
eqcomd |
|
86 |
85
|
3adant3 |
|
87 |
|
simp3 |
|
88 |
86 87
|
eqeltrd |
|
89 |
84 88
|
jca |
|
90 |
77 82 83 89
|
syl3anc |
|
91 |
76 90
|
impbida |
|
92 |
2 91
|
rabbida3 |
|
93 |
12 92
|
eqtrd |
|
94 |
9
|
eleq2i |
|
95 |
94
|
biimpi |
|
96 |
|
rabidim1 |
|
97 |
95 96
|
syl |
|
98 |
97 85
|
sylan2 |
|
99 |
2 93 98
|
mpteq12da |
|
100 |
11 99
|
eqtrd |
|
101 |
|
nfmpt1 |
|
102 |
|
nfcv |
|
103 |
|
nfmpt1 |
|
104 |
102 103
|
nfmpt |
|
105 |
1 8
|
fmptd2f |
|
106 |
|
eqid |
|
107 |
|
eqid |
|
108 |
101 104 4 5 6 105 106 107
|
smfliminf |
|
109 |
100 108
|
eqeltrd |
|