Step |
Hyp |
Ref |
Expression |
1 |
|
xpstopnlem1.f |
|
2 |
|
xpstopnlem1.j |
|
3 |
|
xpstopnlem1.k |
|
4 |
|
txtopon |
|
5 |
2 3 4
|
syl2anc |
|
6 |
|
eqid |
|
7 |
|
0ex |
|
8 |
7
|
a1i |
|
9 |
6 8 2
|
pt1hmeo |
|
10 |
|
hmeocn |
|
11 |
|
cntop2 |
|
12 |
9 10 11
|
3syl |
|
13 |
|
toptopon2 |
|
14 |
12 13
|
sylib |
|
15 |
|
eqid |
|
16 |
|
1on |
|
17 |
16
|
a1i |
|
18 |
15 17 3
|
pt1hmeo |
|
19 |
|
hmeocn |
|
20 |
|
cntop2 |
|
21 |
18 19 20
|
3syl |
|
22 |
|
toptopon2 |
|
23 |
21 22
|
sylib |
|
24 |
|
txtopon |
|
25 |
14 23 24
|
syl2anc |
|
26 |
|
opeq2 |
|
27 |
26
|
sneqd |
|
28 |
|
eqid |
|
29 |
|
snex |
|
30 |
27 28 29
|
fvmpt |
|
31 |
|
opeq2 |
|
32 |
31
|
sneqd |
|
33 |
|
eqid |
|
34 |
|
snex |
|
35 |
32 33 34
|
fvmpt |
|
36 |
|
opeq12 |
|
37 |
30 35 36
|
syl2an |
|
38 |
37
|
mpoeq3ia |
|
39 |
|
toponuni |
|
40 |
2 39
|
syl |
|
41 |
|
toponuni |
|
42 |
3 41
|
syl |
|
43 |
|
mpoeq12 |
|
44 |
40 42 43
|
syl2anc |
|
45 |
38 44
|
syl5eqr |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
46 47 9 18
|
txhmeo |
|
49 |
45 48
|
eqeltrd |
|
50 |
|
hmeocn |
|
51 |
49 50
|
syl |
|
52 |
|
cnf2 |
|
53 |
5 25 51 52
|
syl3anc |
|
54 |
|
eqid |
|
55 |
54
|
fmpo |
|
56 |
53 55
|
sylibr |
|
57 |
56
|
r19.21bi |
|
58 |
57
|
r19.21bi |
|
59 |
58
|
anasss |
|
60 |
|
eqidd |
|
61 |
|
vex |
|
62 |
|
vex |
|
63 |
61 62
|
op1std |
|
64 |
61 62
|
op2ndd |
|
65 |
63 64
|
uneq12d |
|
66 |
65
|
mpompt |
|
67 |
66
|
eqcomi |
|
68 |
67
|
a1i |
|
69 |
29 34
|
op1std |
|
70 |
29 34
|
op2ndd |
|
71 |
69 70
|
uneq12d |
|
72 |
|
df-pr |
|
73 |
71 72
|
eqtr4di |
|
74 |
59 60 68 73
|
fmpoco |
|
75 |
1 74
|
eqtr4id |
|
76 |
|
eqid |
|
77 |
|
eqid |
|
78 |
|
eqid |
|
79 |
|
eqid |
|
80 |
|
eqid |
|
81 |
|
eqid |
|
82 |
|
2on |
|
83 |
82
|
a1i |
|
84 |
|
topontop |
|
85 |
2 84
|
syl |
|
86 |
|
topontop |
|
87 |
3 86
|
syl |
|
88 |
|
xpscf |
|
89 |
85 87 88
|
sylanbrc |
|
90 |
|
df2o3 |
|
91 |
|
df-pr |
|
92 |
90 91
|
eqtri |
|
93 |
92
|
a1i |
|
94 |
|
1n0 |
|
95 |
94
|
necomi |
|
96 |
|
disjsn2 |
|
97 |
95 96
|
mp1i |
|
98 |
76 77 78 79 80 81 83 89 93 97
|
ptunhmeo |
|
99 |
|
fnpr2o |
|
100 |
2 3 99
|
syl2anc |
|
101 |
7
|
prid1 |
|
102 |
101 90
|
eleqtrri |
|
103 |
|
fnressn |
|
104 |
100 102 103
|
sylancl |
|
105 |
|
fvpr0o |
|
106 |
2 105
|
syl |
|
107 |
106
|
opeq2d |
|
108 |
107
|
sneqd |
|
109 |
104 108
|
eqtrd |
|
110 |
109
|
fveq2d |
|
111 |
110
|
unieqd |
|
112 |
|
1oex |
|
113 |
112
|
prid2 |
|
114 |
113 90
|
eleqtrri |
|
115 |
|
fnressn |
|
116 |
100 114 115
|
sylancl |
|
117 |
|
fvpr1o |
|
118 |
3 117
|
syl |
|
119 |
118
|
opeq2d |
|
120 |
119
|
sneqd |
|
121 |
116 120
|
eqtrd |
|
122 |
121
|
fveq2d |
|
123 |
122
|
unieqd |
|
124 |
|
eqidd |
|
125 |
111 123 124
|
mpoeq123dv |
|
126 |
110 122
|
oveq12d |
|
127 |
126
|
oveq1d |
|
128 |
98 125 127
|
3eltr3d |
|
129 |
|
hmeoco |
|
130 |
49 128 129
|
syl2anc |
|
131 |
75 130
|
eqeltrd |
|