Step |
Hyp |
Ref |
Expression |
1 |
|
txdis1cn.x |
|
2 |
|
txdis1cn.j |
|
3 |
|
txdis1cn.k |
|
4 |
|
txdis1cn.f |
|
5 |
|
txdis1cn.1 |
|
6 |
2
|
adantr |
|
7 |
|
toptopon2 |
|
8 |
3 7
|
sylib |
|
9 |
8
|
adantr |
|
10 |
|
cnf2 |
|
11 |
6 9 5 10
|
syl3anc |
|
12 |
|
eqid |
|
13 |
12
|
fmpt |
|
14 |
11 13
|
sylibr |
|
15 |
14
|
ralrimiva |
|
16 |
|
ffnov |
|
17 |
4 15 16
|
sylanbrc |
|
18 |
|
cnvimass |
|
19 |
4
|
adantr |
|
20 |
19
|
fndmd |
|
21 |
18 20
|
sseqtrid |
|
22 |
|
relxp |
|
23 |
|
relss |
|
24 |
21 22 23
|
mpisyl |
|
25 |
|
elpreima |
|
26 |
19 25
|
syl |
|
27 |
|
opelxp |
|
28 |
|
df-ov |
|
29 |
28
|
eqcomi |
|
30 |
29
|
eleq1i |
|
31 |
27 30
|
anbi12i |
|
32 |
|
simprll |
|
33 |
|
snelpwi |
|
34 |
32 33
|
syl |
|
35 |
12
|
mptpreima |
|
36 |
5
|
adantrr |
|
37 |
36
|
ad2ant2r |
|
38 |
|
simplr |
|
39 |
|
cnima |
|
40 |
37 38 39
|
syl2anc |
|
41 |
35 40
|
eqeltrrid |
|
42 |
|
simprlr |
|
43 |
|
simprr |
|
44 |
|
vsnid |
|
45 |
|
opelxp |
|
46 |
44 45
|
mpbiran |
|
47 |
|
oveq2 |
|
48 |
47
|
eleq1d |
|
49 |
48
|
elrab |
|
50 |
46 49
|
bitri |
|
51 |
42 43 50
|
sylanbrc |
|
52 |
|
relxp |
|
53 |
52
|
a1i |
|
54 |
|
opelxp |
|
55 |
32
|
snssd |
|
56 |
55
|
sselda |
|
57 |
56
|
adantrr |
|
58 |
|
elrabi |
|
59 |
58
|
ad2antll |
|
60 |
57 59
|
opelxpd |
|
61 |
|
df-ov |
|
62 |
|
elsni |
|
63 |
62
|
ad2antrl |
|
64 |
63
|
oveq1d |
|
65 |
61 64
|
syl5eqr |
|
66 |
|
oveq2 |
|
67 |
66
|
eleq1d |
|
68 |
67
|
elrab |
|
69 |
68
|
simprbi |
|
70 |
69
|
ad2antll |
|
71 |
65 70
|
eqeltrd |
|
72 |
|
elpreima |
|
73 |
4 72
|
syl |
|
74 |
73
|
ad3antrrr |
|
75 |
60 71 74
|
mpbir2and |
|
76 |
75
|
ex |
|
77 |
54 76
|
syl5bi |
|
78 |
53 77
|
relssdv |
|
79 |
|
xpeq1 |
|
80 |
79
|
eleq2d |
|
81 |
79
|
sseq1d |
|
82 |
80 81
|
anbi12d |
|
83 |
|
xpeq2 |
|
84 |
83
|
eleq2d |
|
85 |
83
|
sseq1d |
|
86 |
84 85
|
anbi12d |
|
87 |
82 86
|
rspc2ev |
|
88 |
34 41 51 78 87
|
syl112anc |
|
89 |
|
opex |
|
90 |
|
eleq1 |
|
91 |
90
|
anbi1d |
|
92 |
91
|
2rexbidv |
|
93 |
89 92
|
elab |
|
94 |
88 93
|
sylibr |
|
95 |
94
|
ex |
|
96 |
31 95
|
syl5bi |
|
97 |
26 96
|
sylbid |
|
98 |
24 97
|
relssdv |
|
99 |
|
ssabral |
|
100 |
98 99
|
sylib |
|
101 |
|
distopon |
|
102 |
1 101
|
syl |
|
103 |
102
|
adantr |
|
104 |
2
|
adantr |
|
105 |
|
eltx |
|
106 |
103 104 105
|
syl2anc |
|
107 |
100 106
|
mpbird |
|
108 |
107
|
ralrimiva |
|
109 |
|
txtopon |
|
110 |
102 2 109
|
syl2anc |
|
111 |
|
iscn |
|
112 |
110 8 111
|
syl2anc |
|
113 |
17 108 112
|
mpbir2and |
|