Step |
Hyp |
Ref |
Expression |
1 |
|
smfinfmpt.n |
|
2 |
|
smfinfmpt.x |
|
3 |
|
smfinfmpt.y |
|
4 |
|
smfinfmpt.m |
|
5 |
|
smfinfmpt.z |
|
6 |
|
smfinfmpt.s |
|
7 |
|
smfinfmpt.b |
|
8 |
|
smfinfmpt.f |
|
9 |
|
smfinfmpt.d |
|
10 |
|
smfinfmpt.g |
|
11 |
10
|
a1i |
|
12 |
9
|
a1i |
|
13 |
|
eqidd |
|
14 |
13 8
|
fvmpt2d |
|
15 |
14
|
dmeqd |
|
16 |
|
nfcv |
|
17 |
|
nfcv |
|
18 |
16 17
|
nfel |
|
19 |
2 18
|
nfan |
|
20 |
|
eqid |
|
21 |
6
|
adantr |
|
22 |
7
|
3expa |
|
23 |
19 21 22 8
|
smffmpt |
|
24 |
23
|
fvmptelrn |
|
25 |
19 20 24
|
dmmptdf |
|
26 |
|
eqidd |
|
27 |
15 25 26
|
3eqtrrd |
|
28 |
1 27
|
iineq2d |
|
29 |
|
nfcv |
|
30 |
|
nfmpt1 |
|
31 |
17 30
|
nfmpt |
|
32 |
31 16
|
nffv |
|
33 |
32
|
nfdm |
|
34 |
17 33
|
nfiin |
|
35 |
29 34
|
rabeqf |
|
36 |
28 35
|
syl |
|
37 |
|
nfv |
|
38 |
3 37
|
nfan |
|
39 |
|
nfcv |
|
40 |
|
nfii1 |
|
41 |
39 40
|
nfel |
|
42 |
1 41
|
nfan |
|
43 |
|
simpll |
|
44 |
|
simpr |
|
45 |
|
eliinid |
|
46 |
45
|
adantll |
|
47 |
27
|
eqcomd |
|
48 |
47
|
adantlr |
|
49 |
46 48
|
eleqtrd |
|
50 |
14
|
fveq1d |
|
51 |
50
|
3adant3 |
|
52 |
|
simp3 |
|
53 |
20
|
fvmpt2 |
|
54 |
52 7 53
|
syl2anc |
|
55 |
51 54
|
eqtr2d |
|
56 |
55
|
breq2d |
|
57 |
43 44 49 56
|
syl3anc |
|
58 |
42 57
|
ralbida |
|
59 |
38 58
|
rexbid |
|
60 |
2 59
|
rabbida |
|
61 |
36 60
|
eqtrd |
|
62 |
12 61
|
eqtrd |
|
63 |
2 62
|
alrimi |
|
64 |
|
nfcv |
|
65 |
|
nfra1 |
|
66 |
64 65
|
nfrex |
|
67 |
|
nfii1 |
|
68 |
66 67
|
nfrabw |
|
69 |
9 68
|
nfcxfr |
|
70 |
39 69
|
nfel |
|
71 |
1 70
|
nfan |
|
72 |
|
simpll |
|
73 |
|
simpr |
|
74 |
9
|
eleq2i |
|
75 |
74
|
biimpi |
|
76 |
|
rabidim1 |
|
77 |
75 76
|
syl |
|
78 |
77
|
adantr |
|
79 |
|
simpr |
|
80 |
|
eliinid |
|
81 |
78 79 80
|
syl2anc |
|
82 |
81
|
adantll |
|
83 |
55
|
idi |
|
84 |
72 73 82 83
|
syl3anc |
|
85 |
71 84
|
mpteq2da |
|
86 |
85
|
rneqd |
|
87 |
86
|
infeq1d |
|
88 |
87
|
ex |
|
89 |
2 88
|
ralrimi |
|
90 |
|
mpteq12f |
|
91 |
63 89 90
|
syl2anc |
|
92 |
11 91
|
eqtrd |
|
93 |
|
nfmpt1 |
|
94 |
|
eqid |
|
95 |
1 8 94
|
fmptdf |
|
96 |
|
eqid |
|
97 |
|
eqid |
|
98 |
93 31 4 5 6 95 96 97
|
smfinf |
|
99 |
92 98
|
eqeltrd |
|