Step |
Hyp |
Ref |
Expression |
1 |
|
efopn.j |
|
2 |
1
|
cnfldtopon |
|
3 |
|
toponss |
|
4 |
2 3
|
mpan |
|
5 |
4
|
sselda |
|
6 |
|
cnxmet |
|
7 |
|
pirp |
|
8 |
1
|
cnfldtopn |
|
9 |
8
|
mopni3 |
|
10 |
7 9
|
mpan2 |
|
11 |
6 10
|
mp3an1 |
|
12 |
|
imass2 |
|
13 |
|
imassrn |
|
14 |
|
eff |
|
15 |
|
frn |
|
16 |
14 15
|
ax-mp |
|
17 |
13 16
|
sstri |
|
18 |
|
sseqin2 |
|
19 |
17 18
|
mpbi |
|
20 |
|
rpxr |
|
21 |
|
blssm |
|
22 |
6 21
|
mp3an1 |
|
23 |
20 22
|
sylan2 |
|
24 |
23
|
ad2antrr |
|
25 |
24
|
sselda |
|
26 |
|
simp-4l |
|
27 |
25 26
|
subcld |
|
28 |
27
|
subid1d |
|
29 |
28
|
fveq2d |
|
30 |
|
0cn |
|
31 |
|
eqid |
|
32 |
31
|
cnmetdval |
|
33 |
27 30 32
|
sylancl |
|
34 |
31
|
cnmetdval |
|
35 |
25 26 34
|
syl2anc |
|
36 |
29 33 35
|
3eqtr4d |
|
37 |
|
simpr |
|
38 |
6
|
a1i |
|
39 |
|
simpllr |
|
40 |
39
|
adantr |
|
41 |
40
|
rpxrd |
|
42 |
|
elbl3 |
|
43 |
38 41 26 25 42
|
syl22anc |
|
44 |
37 43
|
mpbid |
|
45 |
36 44
|
eqbrtrd |
|
46 |
|
0cnd |
|
47 |
|
elbl3 |
|
48 |
38 41 46 27 47
|
syl22anc |
|
49 |
45 48
|
mpbird |
|
50 |
|
efsub |
|
51 |
25 26 50
|
syl2anc |
|
52 |
|
fveqeq2 |
|
53 |
52
|
rspcev |
|
54 |
49 51 53
|
syl2anc |
|
55 |
|
oveq1 |
|
56 |
55
|
eqeq2d |
|
57 |
56
|
rexbidv |
|
58 |
54 57
|
syl5ibcom |
|
59 |
58
|
rexlimdva |
|
60 |
|
eqcom |
|
61 |
|
simplr |
|
62 |
|
simp-4l |
|
63 |
|
efcl |
|
64 |
62 63
|
syl |
|
65 |
39
|
rpxrd |
|
66 |
|
blssm |
|
67 |
6 30 65 66
|
mp3an12i |
|
68 |
67
|
sselda |
|
69 |
|
efcl |
|
70 |
68 69
|
syl |
|
71 |
|
efne0 |
|
72 |
62 71
|
syl |
|
73 |
61 64 70 72
|
divmuld |
|
74 |
60 73
|
syl5bb |
|
75 |
62 68
|
pncan2d |
|
76 |
68
|
subid1d |
|
77 |
75 76
|
eqtr4d |
|
78 |
77
|
fveq2d |
|
79 |
62 68
|
addcld |
|
80 |
31
|
cnmetdval |
|
81 |
79 62 80
|
syl2anc |
|
82 |
31
|
cnmetdval |
|
83 |
68 30 82
|
sylancl |
|
84 |
78 81 83
|
3eqtr4d |
|
85 |
|
simpr |
|
86 |
6
|
a1i |
|
87 |
39
|
adantr |
|
88 |
87
|
rpxrd |
|
89 |
|
0cnd |
|
90 |
|
elbl3 |
|
91 |
86 88 89 68 90
|
syl22anc |
|
92 |
85 91
|
mpbid |
|
93 |
84 92
|
eqbrtrd |
|
94 |
|
elbl3 |
|
95 |
86 88 62 79 94
|
syl22anc |
|
96 |
93 95
|
mpbird |
|
97 |
|
efadd |
|
98 |
62 68 97
|
syl2anc |
|
99 |
|
fveqeq2 |
|
100 |
99
|
rspcev |
|
101 |
96 98 100
|
syl2anc |
|
102 |
|
eqeq2 |
|
103 |
102
|
rexbidv |
|
104 |
101 103
|
syl5ibcom |
|
105 |
74 104
|
sylbid |
|
106 |
105
|
rexlimdva |
|
107 |
59 106
|
impbid |
|
108 |
|
ffn |
|
109 |
14 108
|
ax-mp |
|
110 |
|
fvelimab |
|
111 |
109 24 110
|
sylancr |
|
112 |
|
fvelimab |
|
113 |
109 67 112
|
sylancr |
|
114 |
107 111 113
|
3bitr4d |
|
115 |
114
|
rabbi2dva |
|
116 |
19 115
|
syl5eqr |
|
117 |
|
eqid |
|
118 |
117
|
mptpreima |
|
119 |
116 118
|
eqtr4di |
|
120 |
63
|
ad2antrr |
|
121 |
71
|
ad2antrr |
|
122 |
117
|
divccncf |
|
123 |
120 121 122
|
syl2anc |
|
124 |
1
|
cncfcn1 |
|
125 |
123 124
|
eleqtrdi |
|
126 |
1
|
efopnlem2 |
|
127 |
126
|
adantll |
|
128 |
|
cnima |
|
129 |
125 127 128
|
syl2anc |
|
130 |
119 129
|
eqeltrd |
|
131 |
|
blcntr |
|
132 |
6 131
|
mp3an1 |
|
133 |
|
ffun |
|
134 |
14 133
|
ax-mp |
|
135 |
14
|
fdmi |
|
136 |
23 135
|
sseqtrrdi |
|
137 |
|
funfvima2 |
|
138 |
134 136 137
|
sylancr |
|
139 |
132 138
|
mpd |
|
140 |
139
|
adantr |
|
141 |
|
eleq2 |
|
142 |
|
sseq1 |
|
143 |
141 142
|
anbi12d |
|
144 |
143
|
rspcev |
|
145 |
144
|
expr |
|
146 |
130 140 145
|
syl2anc |
|
147 |
12 146
|
syl5 |
|
148 |
147
|
expimpd |
|
149 |
148
|
rexlimdva |
|
150 |
5 11 149
|
sylc |
|
151 |
150
|
ralrimiva |
|
152 |
|
eleq1 |
|
153 |
152
|
anbi1d |
|
154 |
153
|
rexbidv |
|
155 |
154
|
ralima |
|
156 |
109 4 155
|
sylancr |
|
157 |
151 156
|
mpbird |
|
158 |
1
|
cnfldtop |
|
159 |
|
eltop2 |
|
160 |
158 159
|
ax-mp |
|
161 |
157 160
|
sylibr |
|