Step |
Hyp |
Ref |
Expression |
1 |
|
unbenlem.1 |
|
2 |
|
nnex |
|
3 |
2
|
ssex |
|
4 |
|
1z |
|
5 |
4 1
|
om2uzf1oi |
|
6 |
|
nnuz |
|
7 |
|
f1oeq3 |
|
8 |
6 7
|
ax-mp |
|
9 |
5 8
|
mpbir |
|
10 |
|
f1ocnv |
|
11 |
|
f1of1 |
|
12 |
9 10 11
|
mp2b |
|
13 |
|
f1ores |
|
14 |
12 13
|
mpan |
|
15 |
|
f1oeng |
|
16 |
3 14 15
|
syl2anc |
|
17 |
16
|
adantr |
|
18 |
|
imassrn |
|
19 |
|
dfdm4 |
|
20 |
|
f1of |
|
21 |
9 20
|
ax-mp |
|
22 |
21
|
fdmi |
|
23 |
19 22
|
eqtr3i |
|
24 |
18 23
|
sseqtri |
|
25 |
4 1
|
om2uzuzi |
|
26 |
25 6
|
eleqtrrdi |
|
27 |
|
breq1 |
|
28 |
27
|
rexbidv |
|
29 |
28
|
rspcv |
|
30 |
26 29
|
syl |
|
31 |
30
|
adantr |
|
32 |
|
f1ocnv |
|
33 |
14 32
|
syl |
|
34 |
|
f1ofun |
|
35 |
9 34
|
ax-mp |
|
36 |
|
funcnvres2 |
|
37 |
|
f1oeq1 |
|
38 |
35 36 37
|
mp2b |
|
39 |
33 38
|
sylib |
|
40 |
|
f1ofo |
|
41 |
|
forn |
|
42 |
40 41
|
syl |
|
43 |
42
|
eleq2d |
|
44 |
|
f1ofn |
|
45 |
|
fvelrnb |
|
46 |
44 45
|
syl |
|
47 |
43 46
|
bitr3d |
|
48 |
39 47
|
syl |
|
49 |
48
|
biimpa |
|
50 |
|
fvres |
|
51 |
50
|
eqeq1d |
|
52 |
51
|
biimpa |
|
53 |
52
|
adantll |
|
54 |
24
|
sseli |
|
55 |
4 1
|
om2uzlt2i |
|
56 |
54 55
|
sylan2 |
|
57 |
|
breq2 |
|
58 |
56 57
|
sylan9bb |
|
59 |
53 58
|
syldan |
|
60 |
59
|
biimparc |
|
61 |
60
|
exp44 |
|
62 |
61
|
imp31 |
|
63 |
62
|
reximdva |
|
64 |
49 63
|
syl5 |
|
65 |
64
|
exp4b |
|
66 |
65
|
com4l |
|
67 |
66
|
imp |
|
68 |
67
|
rexlimdv |
|
69 |
31 68
|
syld |
|
70 |
69
|
ex |
|
71 |
70
|
com3l |
|
72 |
71
|
imp |
|
73 |
72
|
ralrimiv |
|
74 |
|
unbnn3 |
|
75 |
24 73 74
|
sylancr |
|
76 |
|
entr |
|
77 |
17 75 76
|
syl2anc |
|