Step |
Hyp |
Ref |
Expression |
1 |
|
elin |
|
2 |
|
eqid |
|
3 |
2
|
ist1 |
|
4 |
3
|
simprbi |
|
5 |
|
onelon |
|
6 |
5
|
ex |
|
7 |
|
neldifsnd |
|
8 |
|
p0ex |
|
9 |
8
|
prid2 |
|
10 |
|
df2o2 |
|
11 |
9 10
|
eleqtrri |
|
12 |
|
elunii |
|
13 |
11 12
|
mpan |
|
14 |
|
df1o2 |
|
15 |
|
1on |
|
16 |
14 15
|
eqeltrri |
|
17 |
16
|
onirri |
|
18 |
17
|
a1i |
|
19 |
13 18
|
eldifd |
|
20 |
19
|
ne0d |
|
21 |
7 20
|
2thd |
|
22 |
|
nbbn |
|
23 |
21 22
|
sylib |
|
24 |
|
on0eln0 |
|
25 |
23 24
|
nsyl |
|
26 |
6 25
|
nsyli |
|
27 |
26
|
imp |
|
28 |
|
0ex |
|
29 |
28
|
prid1 |
|
30 |
29 10
|
eleqtrri |
|
31 |
|
elunii |
|
32 |
30 31
|
mpan |
|
33 |
32
|
adantl |
|
34 |
|
simpr |
|
35 |
34
|
sneqd |
|
36 |
35
|
eleq1d |
|
37 |
33 36
|
rspcdv |
|
38 |
2
|
cldopn |
|
39 |
37 38
|
syl6 |
|
40 |
27 39
|
mtod |
|
41 |
40
|
ex |
|
42 |
41
|
con2d |
|
43 |
4 42
|
syl5 |
|
44 |
|
2on |
|
45 |
|
ontri1 |
|
46 |
|
onsssuc |
|
47 |
45 46
|
bitr3d |
|
48 |
44 47
|
mpan2 |
|
49 |
43 48
|
sylibd |
|
50 |
49
|
imp |
|
51 |
|
0ntop |
|
52 |
|
t1top |
|
53 |
51 52
|
mto |
|
54 |
|
nelneq |
|
55 |
53 54
|
mpan2 |
|
56 |
|
elsni |
|
57 |
55 56
|
nsyl |
|
58 |
57
|
adantl |
|
59 |
50 58
|
eldifd |
|
60 |
1 59
|
sylbi |
|
61 |
60
|
ssriv |
|
62 |
|
df-suc |
|
63 |
62
|
difeq1i |
|
64 |
|
difundir |
|
65 |
63 64
|
eqtri |
|
66 |
|
df-pr |
|
67 |
|
df2o3 |
|
68 |
|
df-pr |
|
69 |
67 68
|
eqtri |
|
70 |
69
|
difeq1i |
|
71 |
|
difundir |
|
72 |
|
difid |
|
73 |
|
1n0 |
|
74 |
|
disjsn2 |
|
75 |
73 74
|
ax-mp |
|
76 |
75
|
difeq2i |
|
77 |
|
difin |
|
78 |
|
dif0 |
|
79 |
76 77 78
|
3eqtr3i |
|
80 |
72 79
|
uneq12i |
|
81 |
|
uncom |
|
82 |
|
un0 |
|
83 |
80 81 82
|
3eqtri |
|
84 |
70 71 83
|
3eqtri |
|
85 |
|
2on0 |
|
86 |
|
disjsn2 |
|
87 |
85 86
|
ax-mp |
|
88 |
87
|
difeq2i |
|
89 |
|
difin |
|
90 |
|
dif0 |
|
91 |
88 89 90
|
3eqtr3i |
|
92 |
84 91
|
uneq12i |
|
93 |
66 92
|
eqtr4i |
|
94 |
65 93
|
eqtr4i |
|
95 |
61 94
|
sseqtri |
|
96 |
|
ssoninhaus |
|
97 |
|
haust1 |
|
98 |
97
|
ssriv |
|
99 |
|
sslin |
|
100 |
98 99
|
ax-mp |
|
101 |
96 100
|
sstri |
|
102 |
95 101
|
eqssi |
|