Step |
Hyp |
Ref |
Expression |
1 |
|
ffn |
|
2 |
|
fnresdm |
|
3 |
1 2
|
syl |
|
4 |
3
|
adantl |
|
5 |
4
|
fveq2d |
|
6 |
|
ssid |
|
7 |
|
sseq1 |
|
8 |
|
reseq2 |
|
9 |
|
res0 |
|
10 |
8 9
|
eqtrdi |
|
11 |
10
|
fveq2d |
|
12 |
11
|
eleq1d |
|
13 |
12
|
imbi2d |
|
14 |
7 13
|
imbi12d |
|
15 |
|
sseq1 |
|
16 |
|
reseq2 |
|
17 |
16
|
fveq2d |
|
18 |
17
|
eleq1d |
|
19 |
18
|
imbi2d |
|
20 |
15 19
|
imbi12d |
|
21 |
|
sseq1 |
|
22 |
|
reseq2 |
|
23 |
22
|
fveq2d |
|
24 |
23
|
eleq1d |
|
25 |
24
|
imbi2d |
|
26 |
21 25
|
imbi12d |
|
27 |
|
sseq1 |
|
28 |
|
reseq2 |
|
29 |
28
|
fveq2d |
|
30 |
29
|
eleq1d |
|
31 |
30
|
imbi2d |
|
32 |
27 31
|
imbi12d |
|
33 |
|
0ex |
|
34 |
|
f0 |
|
35 |
|
pttop |
|
36 |
33 34 35
|
mp2an |
|
37 |
|
eqid |
|
38 |
37
|
ptuni |
|
39 |
33 34 38
|
mp2an |
|
40 |
|
ixp0x |
|
41 |
|
snfi |
|
42 |
40 41
|
eqeltri |
|
43 |
39 42
|
eqeltrri |
|
44 |
|
pwfi |
|
45 |
43 44
|
mpbi |
|
46 |
|
pwuni |
|
47 |
|
ssfi |
|
48 |
45 46 47
|
mp2an |
|
49 |
36 48
|
elini |
|
50 |
|
fincmp |
|
51 |
49 50
|
ax-mp |
|
52 |
51
|
2a1i |
|
53 |
|
ssun1 |
|
54 |
|
id |
|
55 |
53 54
|
sstrid |
|
56 |
55
|
imim1i |
|
57 |
|
eqid |
|
58 |
|
eqid |
|
59 |
|
eqid |
|
60 |
|
resabs1 |
|
61 |
53 60
|
ax-mp |
|
62 |
61
|
eqcomi |
|
63 |
62
|
fveq2i |
|
64 |
|
ssun2 |
|
65 |
|
resabs1 |
|
66 |
64 65
|
ax-mp |
|
67 |
66
|
eqcomi |
|
68 |
67
|
fveq2i |
|
69 |
|
eqid |
|
70 |
|
vex |
|
71 |
|
snex |
|
72 |
70 71
|
unex |
|
73 |
72
|
a1i |
|
74 |
|
simplr |
|
75 |
|
cmptop |
|
76 |
75
|
ssriv |
|
77 |
|
fss |
|
78 |
74 76 77
|
sylancl |
|
79 |
|
simprr |
|
80 |
78 79
|
fssresd |
|
81 |
|
eqidd |
|
82 |
|
simprl |
|
83 |
|
disjsn |
|
84 |
82 83
|
sylibr |
|
85 |
57 58 59 63 68 69 73 80 81 84
|
ptunhmeo |
|
86 |
|
hmphi |
|
87 |
85 86
|
syl |
|
88 |
1
|
ad2antlr |
|
89 |
64 79
|
sstrid |
|
90 |
|
vex |
|
91 |
90
|
snss |
|
92 |
89 91
|
sylibr |
|
93 |
|
fnressn |
|
94 |
88 92 93
|
syl2anc |
|
95 |
94
|
fveq2d |
|
96 |
|
eqid |
|
97 |
90
|
a1i |
|
98 |
74 92
|
ffvelrnd |
|
99 |
76 98
|
sseldi |
|
100 |
|
toptopon2 |
|
101 |
99 100
|
sylib |
|
102 |
96 97 101
|
pt1hmeo |
|
103 |
|
hmphi |
|
104 |
102 103
|
syl |
|
105 |
|
cmphmph |
|
106 |
104 98 105
|
sylc |
|
107 |
95 106
|
eqeltrd |
|
108 |
|
txcmp |
|
109 |
108
|
expcom |
|
110 |
107 109
|
syl |
|
111 |
|
cmphmph |
|
112 |
87 110 111
|
sylsyld |
|
113 |
112
|
expcom |
|
114 |
113
|
a2d |
|
115 |
114
|
ex |
|
116 |
115
|
a2d |
|
117 |
56 116
|
syl5 |
|
118 |
117
|
adantl |
|
119 |
14 20 26 32 52 118
|
findcard2s |
|
120 |
6 119
|
mpi |
|
121 |
120
|
anabsi5 |
|
122 |
5 121
|
eqeltrrd |
|