Step |
Hyp |
Ref |
Expression |
1 |
|
mptsnun.f |
|
2 |
|
mptsnun.r |
|
3 |
|
df-ima |
|
4 |
1
|
reseq1i |
|
5 |
|
resmpt |
|
6 |
4 5
|
syl5eq |
|
7 |
6
|
rneqd |
|
8 |
|
rnmptsn |
|
9 |
7 8
|
eqtrdi |
|
10 |
3 9
|
syl5eq |
|
11 |
10
|
unieqd |
|
12 |
11
|
eleq2d |
|
13 |
|
eleq1w |
|
14 |
|
eluniab |
|
15 |
|
ancom |
|
16 |
|
r19.41v |
|
17 |
|
df-rex |
|
18 |
15 16 17
|
3bitr2i |
|
19 |
|
eleq2 |
|
20 |
19
|
anbi2d |
|
21 |
20
|
adantr |
|
22 |
21
|
ibi |
|
23 |
22
|
anim2i |
|
24 |
23
|
eximi |
|
25 |
18 24
|
sylbi |
|
26 |
|
an12 |
|
27 |
26
|
exbii |
|
28 |
|
exsimpr |
|
29 |
27 28
|
sylbi |
|
30 |
25 29
|
syl |
|
31 |
30
|
exlimiv |
|
32 |
14 31
|
sylbi |
|
33 |
|
velsn |
|
34 |
33
|
anbi2i |
|
35 |
34
|
exbii |
|
36 |
32 35
|
sylib |
|
37 |
13
|
biimparc |
|
38 |
37
|
exlimiv |
|
39 |
36 38
|
syl |
|
40 |
13 39
|
vtoclga |
|
41 |
|
equid |
|
42 |
|
eqid |
|
43 |
|
snex |
|
44 |
|
sbcg |
|
45 |
43 44
|
ax-mp |
|
46 |
|
eqsbc3 |
|
47 |
43 46
|
ax-mp |
|
48 |
19
|
adantl |
|
49 |
|
df-rex |
|
50 |
14
|
biimpri |
|
51 |
50
|
19.23bi |
|
52 |
51
|
expcom |
|
53 |
49 52
|
sylbir |
|
54 |
53
|
19.23bi |
|
55 |
48 54
|
sylbird |
|
56 |
55
|
sbcth |
|
57 |
43 56
|
ax-mp |
|
58 |
|
sbcimg |
|
59 |
43 58
|
ax-mp |
|
60 |
57 59
|
mpbi |
|
61 |
|
sbcan |
|
62 |
|
nfv |
|
63 |
|
nfab1 |
|
64 |
63
|
nfuni |
|
65 |
64
|
nfcri |
|
66 |
62 65
|
nfim |
|
67 |
43 66
|
sbcgfi |
|
68 |
60 61 67
|
3imtr3i |
|
69 |
45 47 68
|
syl2anbr |
|
70 |
42 69
|
mpan2 |
|
71 |
33 70
|
syl5bir |
|
72 |
|
eleq1w |
|
73 |
71 72
|
mpbidi |
|
74 |
73
|
com12 |
|
75 |
74
|
sbimi |
|
76 |
|
equsb3 |
|
77 |
|
sbv |
|
78 |
75 76 77
|
3imtr3i |
|
79 |
41 78
|
ax-mp |
|
80 |
40 79
|
impbii |
|
81 |
12 80
|
syl6bb |
|
82 |
81
|
eqrdv |
|
83 |
82
|
eqcomd |
|