Step |
Hyp |
Ref |
Expression |
1 |
|
bcth.2 |
|
2 |
|
cmetmet |
|
3 |
|
metxmet |
|
4 |
2 3
|
syl |
|
5 |
1
|
mopntop |
|
6 |
5
|
ad2antrr |
|
7 |
|
ffvelrn |
|
8 |
|
elssuni |
|
9 |
7 8
|
syl |
|
10 |
9
|
adantll |
|
11 |
|
eqid |
|
12 |
11
|
clsval2 |
|
13 |
6 10 12
|
syl2anc |
|
14 |
1
|
mopnuni |
|
15 |
14
|
ad2antrr |
|
16 |
13 15
|
eqeq12d |
|
17 |
|
difeq2 |
|
18 |
|
difid |
|
19 |
17 18
|
eqtrdi |
|
20 |
|
difss |
|
21 |
11
|
ntropn |
|
22 |
6 20 21
|
sylancl |
|
23 |
|
elssuni |
|
24 |
22 23
|
syl |
|
25 |
|
dfss4 |
|
26 |
24 25
|
sylib |
|
27 |
|
id |
|
28 |
|
elfvdm |
|
29 |
|
difexg |
|
30 |
28 29
|
syl |
|
31 |
30
|
adantr |
|
32 |
|
fveq2 |
|
33 |
32
|
difeq2d |
|
34 |
|
eqid |
|
35 |
33 34
|
fvmptg |
|
36 |
27 31 35
|
syl2anr |
|
37 |
15
|
difeq1d |
|
38 |
36 37
|
eqtrd |
|
39 |
38
|
fveq2d |
|
40 |
26 39
|
eqtr4d |
|
41 |
40
|
eqeq1d |
|
42 |
19 41
|
syl5ib |
|
43 |
16 42
|
sylbid |
|
44 |
43
|
ralimdva |
|
45 |
4 44
|
sylan |
|
46 |
|
ffvelrn |
|
47 |
14
|
difeq1d |
|
48 |
47
|
adantr |
|
49 |
11
|
opncld |
|
50 |
5 49
|
sylan |
|
51 |
48 50
|
eqeltrd |
|
52 |
46 51
|
sylan2 |
|
53 |
52
|
anassrs |
|
54 |
53
|
ralrimiva |
|
55 |
4 54
|
sylan |
|
56 |
34
|
fmpt |
|
57 |
55 56
|
sylib |
|
58 |
|
nne |
|
59 |
58
|
ralbii |
|
60 |
|
ralnex |
|
61 |
59 60
|
bitr3i |
|
62 |
1
|
bcth |
|
63 |
62
|
3expia |
|
64 |
63
|
necon1bd |
|
65 |
61 64
|
syl5bi |
|
66 |
57 65
|
syldan |
|
67 |
|
difeq2 |
|
68 |
|
difexg |
|
69 |
28 68
|
syl |
|
70 |
69
|
ad2antrr |
|
71 |
70
|
ralrimiva |
|
72 |
34
|
fnmpt |
|
73 |
|
fniunfv |
|
74 |
71 72 73
|
3syl |
|
75 |
36
|
iuneq2dv |
|
76 |
33
|
cbviunv |
|
77 |
75 76
|
eqtr4di |
|
78 |
74 77
|
eqtr3d |
|
79 |
|
iundif2 |
|
80 |
78 79
|
eqtrdi |
|
81 |
|
ffn |
|
82 |
81
|
adantl |
|
83 |
|
fniinfv |
|
84 |
82 83
|
syl |
|
85 |
84
|
difeq2d |
|
86 |
14
|
adantr |
|
87 |
86
|
difeq1d |
|
88 |
80 85 87
|
3eqtrd |
|
89 |
88
|
fveq2d |
|
90 |
89
|
difeq2d |
|
91 |
5
|
adantr |
|
92 |
|
1nn |
|
93 |
|
biidd |
|
94 |
|
fnfvelrn |
|
95 |
82 94
|
sylan |
|
96 |
|
intss1 |
|
97 |
95 96
|
syl |
|
98 |
97 10
|
sstrd |
|
99 |
98
|
expcom |
|
100 |
93 99
|
vtoclga |
|
101 |
92 100
|
ax-mp |
|
102 |
11
|
clsval2 |
|
103 |
91 101 102
|
syl2anc |
|
104 |
90 103
|
eqtr4d |
|
105 |
|
dif0 |
|
106 |
105 86
|
eqtr4id |
|
107 |
104 106
|
eqeq12d |
|
108 |
67 107
|
syl5ib |
|
109 |
4 108
|
sylan |
|
110 |
45 66 109
|
3syld |
|
111 |
110
|
3impia |
|