Step |
Hyp |
Ref |
Expression |
1 |
|
simplr |
|
2 |
|
fzfi |
|
3 |
|
difinf |
|
4 |
1 2 3
|
sylancl |
|
5 |
|
fzfi |
|
6 |
|
diffi |
|
7 |
5 6
|
ax-mp |
|
8 |
|
isinffi |
|
9 |
4 7 8
|
sylancl |
|
10 |
|
f1f1orn |
|
11 |
10
|
adantl |
|
12 |
|
f1oi |
|
13 |
12
|
a1i |
|
14 |
|
incom |
|
15 |
|
disjdif |
|
16 |
14 15
|
eqtri |
|
17 |
16
|
a1i |
|
18 |
|
f1f |
|
19 |
18
|
frnd |
|
20 |
19
|
adantl |
|
21 |
20
|
ssrind |
|
22 |
|
incom |
|
23 |
|
disjdif |
|
24 |
22 23
|
eqtri |
|
25 |
21 24
|
sseqtrdi |
|
26 |
|
ss0 |
|
27 |
25 26
|
syl |
|
28 |
|
f1oun |
|
29 |
11 13 17 27 28
|
syl22anc |
|
30 |
|
f1of1 |
|
31 |
29 30
|
syl |
|
32 |
|
uncom |
|
33 |
|
simplrr |
|
34 |
|
fzss2 |
|
35 |
33 34
|
syl |
|
36 |
|
undif |
|
37 |
35 36
|
sylib |
|
38 |
32 37
|
syl5eq |
|
39 |
|
f1eq2 |
|
40 |
38 39
|
syl |
|
41 |
31 40
|
mpbid |
|
42 |
19
|
difss2d |
|
43 |
42
|
adantl |
|
44 |
|
simplrl |
|
45 |
43 44
|
unssd |
|
46 |
|
f1ss |
|
47 |
41 45 46
|
syl2anc |
|
48 |
|
resundir |
|
49 |
|
dmres |
|
50 |
|
incom |
|
51 |
|
f1dm |
|
52 |
51
|
adantl |
|
53 |
52
|
ineq1d |
|
54 |
53 16
|
eqtrdi |
|
55 |
50 54
|
syl5eq |
|
56 |
49 55
|
syl5eq |
|
57 |
|
relres |
|
58 |
|
reldm0 |
|
59 |
57 58
|
ax-mp |
|
60 |
56 59
|
sylibr |
|
61 |
|
residm |
|
62 |
61
|
a1i |
|
63 |
60 62
|
uneq12d |
|
64 |
|
uncom |
|
65 |
|
un0 |
|
66 |
64 65
|
eqtri |
|
67 |
63 66
|
eqtrdi |
|
68 |
48 67
|
syl5eq |
|
69 |
|
vex |
|
70 |
|
ovex |
|
71 |
|
resiexg |
|
72 |
70 71
|
ax-mp |
|
73 |
69 72
|
unex |
|
74 |
|
f1eq1 |
|
75 |
|
reseq1 |
|
76 |
75
|
eqeq1d |
|
77 |
74 76
|
anbi12d |
|
78 |
73 77
|
spcev |
|
79 |
47 68 78
|
syl2anc |
|
80 |
9 79
|
exlimddv |
|