Step |
Hyp |
Ref |
Expression |
1 |
|
smfpimcc.1 |
|
2 |
|
smfpimcc.z |
|
3 |
|
smfpimcc.s |
|
4 |
|
smfpimcc.f |
|
5 |
|
smfpimcc.j |
|
6 |
|
smfpimcc.b |
|
7 |
|
smfpimcc.a |
|
8 |
2
|
uzct |
|
9 |
8
|
a1i |
|
10 |
|
mptct |
|
11 |
|
rnct |
|
12 |
9 10 11
|
3syl |
|
13 |
|
vex |
|
14 |
|
eqid |
|
15 |
14
|
elrnmpt |
|
16 |
13 15
|
ax-mp |
|
17 |
16
|
biimpi |
|
18 |
17
|
adantl |
|
19 |
|
simp3 |
|
20 |
3
|
adantr |
|
21 |
4
|
ffvelrnda |
|
22 |
|
eqid |
|
23 |
7
|
adantr |
|
24 |
|
eqid |
|
25 |
20 21 22 5 6 23 24
|
smfpimbor1 |
|
26 |
|
fvex |
|
27 |
26
|
dmex |
|
28 |
27
|
a1i |
|
29 |
|
elrest |
|
30 |
3 28 29
|
syl2anc |
|
31 |
30
|
adantr |
|
32 |
25 31
|
mpbid |
|
33 |
|
rabn0 |
|
34 |
32 33
|
sylibr |
|
35 |
34
|
3adant3 |
|
36 |
19 35
|
eqnetrd |
|
37 |
36
|
3exp |
|
38 |
37
|
rexlimdv |
|
39 |
38
|
adantr |
|
40 |
18 39
|
mpd |
|
41 |
12 40
|
axccd2 |
|
42 |
|
nfv |
|
43 |
|
nfmpt1 |
|
44 |
43
|
nfrn |
|
45 |
|
nfv |
|
46 |
44 45
|
nfralw |
|
47 |
42 46
|
nfan |
|
48 |
2
|
fvexi |
|
49 |
3
|
adantr |
|
50 |
|
fveq2 |
|
51 |
|
id |
|
52 |
50 51
|
eleq12d |
|
53 |
52
|
rspccva |
|
54 |
53
|
adantll |
|
55 |
|
eqid |
|
56 |
47 48 49 54 55
|
smfpimcclem |
|
57 |
56
|
ex |
|
58 |
57
|
exlimdv |
|
59 |
41 58
|
mpd |
|
60 |
|
nfcv |
|
61 |
1 60
|
nffv |
|
62 |
61
|
nfcnv |
|
63 |
|
nfcv |
|
64 |
62 63
|
nfima |
|
65 |
|
nfcv |
|
66 |
61
|
nfdm |
|
67 |
65 66
|
nfin |
|
68 |
64 67
|
nfeq |
|
69 |
|
nfv |
|
70 |
|
fveq2 |
|
71 |
70
|
cnveqd |
|
72 |
71
|
imaeq1d |
|
73 |
|
fveq2 |
|
74 |
70
|
dmeqd |
|
75 |
73 74
|
ineq12d |
|
76 |
72 75
|
eqeq12d |
|
77 |
68 69 76
|
cbvralw |
|
78 |
77
|
anbi2i |
|
79 |
78
|
exbii |
|
80 |
59 79
|
sylib |
|