Step |
Hyp |
Ref |
Expression |
1 |
|
xkohmeo.x |
|
2 |
|
xkohmeo.y |
|
3 |
|
xkohmeo.f |
|
4 |
|
xkohmeo.j |
|
5 |
|
xkohmeo.k |
|
6 |
|
xkohmeo.l |
|
7 |
|
txtopon |
|
8 |
1 2 7
|
syl2anc |
|
9 |
|
topontop |
|
10 |
8 9
|
syl |
|
11 |
|
eqid |
|
12 |
11
|
xkotopon |
|
13 |
10 6 12
|
syl2anc |
|
14 |
|
vex |
|
15 |
|
vex |
|
16 |
14 15
|
op1std |
|
17 |
14 15
|
op2ndd |
|
18 |
|
eqidd |
|
19 |
16 17 18
|
oveq123d |
|
20 |
19
|
mpteq2dv |
|
21 |
20
|
mpompt |
|
22 |
|
txtopon |
|
23 |
13 1 22
|
syl2anc |
|
24 |
|
vex |
|
25 |
|
vex |
|
26 |
24 25
|
op1std |
|
27 |
26
|
fveq2d |
|
28 |
26
|
fveq2d |
|
29 |
24 25
|
op2ndd |
|
30 |
27 28 29
|
oveq123d |
|
31 |
30
|
mpompt |
|
32 |
|
txtopon |
|
33 |
23 2 32
|
syl2anc |
|
34 |
|
toptopon2 |
|
35 |
6 34
|
sylib |
|
36 |
|
txcmp |
|
37 |
36
|
txnlly |
|
38 |
4 5 37
|
syl2anc |
|
39 |
27
|
mpompt |
|
40 |
8
|
adantr |
|
41 |
35
|
adantr |
|
42 |
|
xp1st |
|
43 |
42
|
adantl |
|
44 |
|
xp1st |
|
45 |
43 44
|
syl |
|
46 |
|
cnf2 |
|
47 |
40 41 45 46
|
syl3anc |
|
48 |
47
|
feqmptd |
|
49 |
48
|
mpteq2dva |
|
50 |
39 49
|
syl5eqr |
|
51 |
23 2
|
cnmpt1st |
|
52 |
|
fveq2 |
|
53 |
52
|
cbvmptv |
|
54 |
16
|
mpompt |
|
55 |
13 1
|
cnmpt1st |
|
56 |
54 55
|
eqeltrid |
|
57 |
53 56
|
eqeltrid |
|
58 |
23 2 51 23 57 52
|
cnmpt21 |
|
59 |
50 58
|
eqeltrrd |
|
60 |
28
|
mpompt |
|
61 |
|
fveq2 |
|
62 |
61
|
cbvmptv |
|
63 |
17
|
mpompt |
|
64 |
13 1
|
cnmpt2nd |
|
65 |
63 64
|
eqeltrid |
|
66 |
62 65
|
eqeltrid |
|
67 |
23 2 51 23 66 61
|
cnmpt21 |
|
68 |
60 67
|
eqeltrid |
|
69 |
29
|
mpompt |
|
70 |
23 2
|
cnmpt2nd |
|
71 |
69 70
|
eqeltrid |
|
72 |
33 68 71
|
cnmpt1t |
|
73 |
|
fveq2 |
|
74 |
|
df-ov |
|
75 |
73 74
|
eqtr4di |
|
76 |
33 8 35 38 59 72 75
|
cnmptk1p |
|
77 |
31 76
|
eqeltrrid |
|
78 |
23 2 77
|
cnmpt2k |
|
79 |
21 78
|
eqeltrrid |
|
80 |
13 1 79
|
cnmpt2k |
|
81 |
3 80
|
eqeltrid |
|
82 |
1 2 3 4 5 6
|
xkocnv |
|
83 |
15 25
|
op1std |
|
84 |
83
|
fveq2d |
|
85 |
15 25
|
op2ndd |
|
86 |
84 85
|
fveq12d |
|
87 |
86
|
mpompt |
|
88 |
87
|
mpteq2i |
|
89 |
82 88
|
eqtr4di |
|
90 |
|
nllytop |
|
91 |
4 90
|
syl |
|
92 |
|
nllytop |
|
93 |
5 92
|
syl |
|
94 |
|
xkotop |
|
95 |
93 6 94
|
syl2anc |
|
96 |
|
eqid |
|
97 |
96
|
xkotopon |
|
98 |
91 95 97
|
syl2anc |
|
99 |
|
vex |
|
100 |
99 24
|
op1std |
|
101 |
99 24
|
op2ndd |
|
102 |
101
|
fveq2d |
|
103 |
100 102
|
fveq12d |
|
104 |
101
|
fveq2d |
|
105 |
103 104
|
fveq12d |
|
106 |
105
|
mpompt |
|
107 |
|
txtopon |
|
108 |
98 8 107
|
syl2anc |
|
109 |
2
|
adantr |
|
110 |
35
|
adantr |
|
111 |
|
eqid |
|
112 |
111
|
xkotopon |
|
113 |
93 6 112
|
syl2anc |
|
114 |
|
xp1st |
|
115 |
|
cnf2 |
|
116 |
1 113 114 115
|
syl2an3an |
|
117 |
|
xp2nd |
|
118 |
117
|
adantl |
|
119 |
|
xp1st |
|
120 |
118 119
|
syl |
|
121 |
116 120
|
ffvelrnd |
|
122 |
|
cnf2 |
|
123 |
109 110 121 122
|
syl3anc |
|
124 |
123
|
feqmptd |
|
125 |
124
|
mpteq2dva |
|
126 |
100
|
mpompt |
|
127 |
116
|
feqmptd |
|
128 |
127
|
mpteq2dva |
|
129 |
126 128
|
syl5eqr |
|
130 |
98 8
|
cnmpt1st |
|
131 |
129 130
|
eqeltrrd |
|
132 |
102
|
mpompt |
|
133 |
98 8
|
cnmpt2nd |
|
134 |
52
|
cbvmptv |
|
135 |
83
|
mpompt |
|
136 |
1 2
|
cnmpt1st |
|
137 |
135 136
|
eqeltrid |
|
138 |
134 137
|
eqeltrid |
|
139 |
98 8 133 8 138 52
|
cnmpt21 |
|
140 |
132 139
|
eqeltrid |
|
141 |
|
fveq2 |
|
142 |
108 1 113 4 131 140 141
|
cnmptk1p |
|
143 |
125 142
|
eqeltrrd |
|
144 |
104
|
mpompt |
|
145 |
61
|
cbvmptv |
|
146 |
85
|
mpompt |
|
147 |
1 2
|
cnmpt2nd |
|
148 |
146 147
|
eqeltrid |
|
149 |
145 148
|
eqeltrid |
|
150 |
98 8 133 8 149 61
|
cnmpt21 |
|
151 |
144 150
|
eqeltrid |
|
152 |
|
fveq2 |
|
153 |
108 2 35 5 143 151 152
|
cnmptk1p |
|
154 |
106 153
|
eqeltrrid |
|
155 |
98 8 154
|
cnmpt2k |
|
156 |
89 155
|
eqeltrd |
|
157 |
|
ishmeo |
|
158 |
81 156 157
|
sylanbrc |
|