Step |
Hyp |
Ref |
Expression |
1 |
|
hausdiag.x |
|
2 |
1
|
ishaus |
|
3 |
|
txtop |
|
4 |
3
|
anidms |
|
5 |
|
idssxp |
|
6 |
1 1
|
txuni |
|
7 |
6
|
anidms |
|
8 |
5 7
|
sseqtrid |
|
9 |
|
eqid |
|
10 |
9
|
iscld2 |
|
11 |
4 8 10
|
syl2anc |
|
12 |
|
eltx |
|
13 |
12
|
anidms |
|
14 |
|
eldif |
|
15 |
7
|
eqcomd |
|
16 |
15
|
eleq2d |
|
17 |
16
|
anbi1d |
|
18 |
14 17
|
syl5bb |
|
19 |
18
|
imbi1d |
|
20 |
|
impexp |
|
21 |
19 20
|
bitrdi |
|
22 |
21
|
ralbidv2 |
|
23 |
|
eleq1 |
|
24 |
23
|
notbid |
|
25 |
|
eleq1 |
|
26 |
25
|
anbi1d |
|
27 |
26
|
2rexbidv |
|
28 |
24 27
|
imbi12d |
|
29 |
28
|
ralxp |
|
30 |
22 29
|
bitrdi |
|
31 |
|
vex |
|
32 |
31
|
opelresi |
|
33 |
|
ibar |
|
34 |
33
|
adantr |
|
35 |
|
df-br |
|
36 |
31
|
ideq |
|
37 |
35 36
|
bitr3i |
|
38 |
34 37
|
bitr3di |
|
39 |
32 38
|
syl5bb |
|
40 |
39
|
adantl |
|
41 |
40
|
necon3bbid |
|
42 |
|
elssuni |
|
43 |
|
elssuni |
|
44 |
|
xpss12 |
|
45 |
42 43 44
|
syl2an |
|
46 |
1 1
|
xpeq12i |
|
47 |
45 46
|
sseqtrrdi |
|
48 |
47
|
adantl |
|
49 |
7
|
ad2antrr |
|
50 |
48 49
|
sseqtrd |
|
51 |
|
reldisj |
|
52 |
50 51
|
syl |
|
53 |
|
df-res |
|
54 |
53
|
ineq2i |
|
55 |
|
inass |
|
56 |
|
inss1 |
|
57 |
56 48
|
sstrid |
|
58 |
|
ssv |
|
59 |
|
xpss2 |
|
60 |
58 59
|
ax-mp |
|
61 |
57 60
|
sstrdi |
|
62 |
|
df-ss |
|
63 |
61 62
|
sylib |
|
64 |
55 63
|
syl5eqr |
|
65 |
54 64
|
syl5eq |
|
66 |
65
|
eqeq1d |
|
67 |
|
opelxp |
|
68 |
|
df-br |
|
69 |
|
elin |
|
70 |
67 68 69
|
3bitr4i |
|
71 |
70
|
notbii |
|
72 |
71
|
albii |
|
73 |
|
intirr |
|
74 |
|
eq0 |
|
75 |
72 73 74
|
3bitr4i |
|
76 |
66 75
|
bitrdi |
|
77 |
52 76
|
bitr3d |
|
78 |
77
|
anbi2d |
|
79 |
|
opelxp |
|
80 |
79
|
anbi1i |
|
81 |
|
df-3an |
|
82 |
78 80 81
|
3bitr4g |
|
83 |
82
|
2rexbidva |
|
84 |
41 83
|
imbi12d |
|
85 |
84
|
2ralbidva |
|
86 |
30 85
|
bitrd |
|
87 |
11 13 86
|
3bitrrd |
|
88 |
87
|
pm5.32i |
|
89 |
2 88
|
bitri |
|