Step |
Hyp |
Ref |
Expression |
1 |
|
qtopcmp.1 |
|
2 |
|
f1ocnv |
|
3 |
|
f1ofun |
|
4 |
2 3
|
syl |
|
5 |
4
|
ad2antlr |
|
6 |
|
simpr |
|
7 |
|
df-rn |
|
8 |
|
f1ofo |
|
9 |
8
|
ad2antlr |
|
10 |
|
forn |
|
11 |
9 10
|
syl |
|
12 |
7 11
|
eqtr3id |
|
13 |
6 12
|
sseqtrrd |
|
14 |
|
funimass4 |
|
15 |
5 13 14
|
syl2anc |
|
16 |
|
dfss3 |
|
17 |
|
simprl |
|
18 |
17
|
elin1d |
|
19 |
1
|
elqtop2 |
|
20 |
8 19
|
sylan2 |
|
21 |
20
|
ad3antrrr |
|
22 |
18 21
|
mpbid |
|
23 |
22
|
simprd |
|
24 |
17
|
elin2d |
|
25 |
24
|
elpwid |
|
26 |
|
imass2 |
|
27 |
25 26
|
syl |
|
28 |
23 27
|
elpwd |
|
29 |
23 28
|
elind |
|
30 |
|
simp-4r |
|
31 |
30 2
|
syl |
|
32 |
|
f1ofn |
|
33 |
31 32
|
syl |
|
34 |
6
|
ad2antrr |
|
35 |
25 34
|
sstrd |
|
36 |
|
simprr |
|
37 |
|
fnfvima |
|
38 |
33 35 36 37
|
syl3anc |
|
39 |
|
eleq2 |
|
40 |
39
|
rspcev |
|
41 |
29 38 40
|
syl2anc |
|
42 |
41
|
rexlimdvaa |
|
43 |
|
simp-4r |
|
44 |
|
f1ofun |
|
45 |
43 44
|
syl |
|
46 |
|
simprl |
|
47 |
46
|
elin2d |
|
48 |
47
|
elpwid |
|
49 |
|
funimass2 |
|
50 |
45 48 49
|
syl2anc |
|
51 |
6
|
ad2antrr |
|
52 |
50 51
|
sstrd |
|
53 |
|
f1of1 |
|
54 |
43 53
|
syl |
|
55 |
46
|
elin1d |
|
56 |
|
elssuni |
|
57 |
56 1
|
sseqtrrdi |
|
58 |
55 57
|
syl |
|
59 |
|
f1imacnv |
|
60 |
54 58 59
|
syl2anc |
|
61 |
60 55
|
eqeltrd |
|
62 |
1
|
elqtop2 |
|
63 |
8 62
|
sylan2 |
|
64 |
63
|
ad3antrrr |
|
65 |
52 61 64
|
mpbir2and |
|
66 |
|
vex |
|
67 |
66
|
elpw2 |
|
68 |
50 67
|
sylibr |
|
69 |
65 68
|
elind |
|
70 |
6
|
sselda |
|
71 |
70
|
adantr |
|
72 |
|
f1ocnvfv2 |
|
73 |
43 71 72
|
syl2anc |
|
74 |
|
f1ofn |
|
75 |
74
|
adantl |
|
76 |
75
|
ad3antrrr |
|
77 |
|
simprr |
|
78 |
|
fnfvima |
|
79 |
76 58 77 78
|
syl3anc |
|
80 |
73 79
|
eqeltrrd |
|
81 |
|
eleq2 |
|
82 |
81
|
rspcev |
|
83 |
69 80 82
|
syl2anc |
|
84 |
83
|
rexlimdvaa |
|
85 |
42 84
|
impbid |
|
86 |
|
eluni2 |
|
87 |
|
eluni2 |
|
88 |
85 86 87
|
3bitr4g |
|
89 |
88
|
ralbidva |
|
90 |
16 89
|
syl5bb |
|
91 |
15 90
|
bitr4d |
|
92 |
|
eltg |
|
93 |
92
|
ad2antrr |
|
94 |
|
ovex |
|
95 |
|
eltg |
|
96 |
94 95
|
mp1i |
|
97 |
91 93 96
|
3bitr4d |
|
98 |
97
|
pm5.32da |
|
99 |
|
tgtopon |
|
100 |
99
|
adantr |
|
101 |
1
|
fveq2i |
|
102 |
100 101
|
eleqtrrdi |
|
103 |
8
|
adantl |
|
104 |
|
elqtop3 |
|
105 |
102 103 104
|
syl2anc |
|
106 |
|
unitg |
|
107 |
94 106
|
ax-mp |
|
108 |
1
|
elqtop2 |
|
109 |
8 108
|
sylan2 |
|
110 |
|
simpl |
|
111 |
|
velpw |
|
112 |
110 111
|
sylibr |
|
113 |
109 112
|
syl6bi |
|
114 |
113
|
ssrdv |
|
115 |
|
sspwuni |
|
116 |
114 115
|
sylib |
|
117 |
107 116
|
eqsstrid |
|
118 |
|
sspwuni |
|
119 |
117 118
|
sylibr |
|
120 |
119
|
sseld |
|
121 |
120 111
|
syl6ib |
|
122 |
121
|
pm4.71rd |
|
123 |
98 105 122
|
3bitr4d |
|
124 |
123
|
eqrdv |
|