Step |
Hyp |
Ref |
Expression |
1 |
|
ptcls.2 |
|
2 |
|
ptcls.a |
|
3 |
|
ptcls.j |
|
4 |
|
ptcls.c |
|
5 |
|
ptclsg.1 |
|
6 |
|
topontop |
|
7 |
3 6
|
syl |
|
8 |
|
toponuni |
|
9 |
3 8
|
syl |
|
10 |
4 9
|
sseqtrd |
|
11 |
|
eqid |
|
12 |
11
|
clscld |
|
13 |
7 10 12
|
syl2anc |
|
14 |
2 7 13
|
ptcldmpt |
|
15 |
1
|
fveq2i |
|
16 |
14 15
|
eleqtrrdi |
|
17 |
11
|
sscls |
|
18 |
7 10 17
|
syl2anc |
|
19 |
18
|
ralrimiva |
|
20 |
|
ss2ixp |
|
21 |
19 20
|
syl |
|
22 |
|
eqid |
|
23 |
22
|
clsss2 |
|
24 |
16 21 23
|
syl2anc |
|
25 |
|
vex |
|
26 |
|
eqeq1 |
|
27 |
26
|
anbi2d |
|
28 |
27
|
exbidv |
|
29 |
25 28
|
elab |
|
30 |
|
nffvmpt1 |
|
31 |
30
|
nfel2 |
|
32 |
|
nfv |
|
33 |
|
fveq2 |
|
34 |
|
fveq2 |
|
35 |
33 34
|
eleq12d |
|
36 |
31 32 35
|
cbvralw |
|
37 |
|
simpr |
|
38 |
|
eqid |
|
39 |
38
|
fvmpt2 |
|
40 |
37 3 39
|
syl2anc |
|
41 |
40
|
eleq2d |
|
42 |
41
|
ralbidva |
|
43 |
36 42
|
syl5bb |
|
44 |
43
|
anbi2d |
|
45 |
44
|
adantr |
|
46 |
45
|
biimpa |
|
47 |
5
|
ad2antrr |
|
48 |
|
simpll |
|
49 |
|
vex |
|
50 |
49
|
elixp |
|
51 |
50
|
simprbi |
|
52 |
51
|
ad2antlr |
|
53 |
11
|
clsndisj |
|
54 |
53
|
ex |
|
55 |
54
|
3expia |
|
56 |
7 10 55
|
syl2anc |
|
57 |
56
|
ralimdva |
|
58 |
48 52 57
|
sylc |
|
59 |
|
simprlr |
|
60 |
|
simprr |
|
61 |
33
|
cbvixpv |
|
62 |
60 61
|
eleqtrdi |
|
63 |
49
|
elixp |
|
64 |
63
|
simprbi |
|
65 |
62 64
|
syl |
|
66 |
|
r19.26 |
|
67 |
59 65 66
|
sylanbrc |
|
68 |
|
ralim |
|
69 |
58 67 68
|
sylc |
|
70 |
|
rabn0 |
|
71 |
|
dfin5 |
|
72 |
|
inss2 |
|
73 |
|
ssiun2 |
|
74 |
72 73
|
sstrid |
|
75 |
|
sseqin2 |
|
76 |
74 75
|
sylib |
|
77 |
71 76
|
syl5eqr |
|
78 |
77
|
neeq1d |
|
79 |
70 78
|
bitr3id |
|
80 |
79
|
ralbiia |
|
81 |
69 80
|
sylibr |
|
82 |
|
nfv |
|
83 |
|
nfiu1 |
|
84 |
|
nfcv |
|
85 |
|
nfcsb1v |
|
86 |
84 85
|
nfin |
|
87 |
86
|
nfel2 |
|
88 |
83 87
|
nfrex |
|
89 |
|
fveq2 |
|
90 |
|
csbeq1a |
|
91 |
89 90
|
ineq12d |
|
92 |
91
|
eleq2d |
|
93 |
92
|
rexbidv |
|
94 |
82 88 93
|
cbvralw |
|
95 |
81 94
|
sylib |
|
96 |
|
eleq1 |
|
97 |
96
|
acni3 |
|
98 |
47 95 97
|
syl2anc |
|
99 |
|
ffn |
|
100 |
|
nfv |
|
101 |
86
|
nfel2 |
|
102 |
|
fveq2 |
|
103 |
102 91
|
eleq12d |
|
104 |
100 101 103
|
cbvralw |
|
105 |
|
ne0i |
|
106 |
|
vex |
|
107 |
106
|
elixp |
|
108 |
|
ixpin |
|
109 |
61
|
ineq1i |
|
110 |
108 109
|
eqtr4i |
|
111 |
110
|
neeq1i |
|
112 |
105 107 111
|
3imtr3i |
|
113 |
104 112
|
sylan2br |
|
114 |
99 113
|
sylan |
|
115 |
114
|
exlimiv |
|
116 |
98 115
|
syl |
|
117 |
116
|
expr |
|
118 |
46 117
|
syldan |
|
119 |
118
|
3adantr3 |
|
120 |
|
eleq2 |
|
121 |
|
ineq1 |
|
122 |
121
|
neeq1d |
|
123 |
120 122
|
imbi12d |
|
124 |
119 123
|
syl5ibrcom |
|
125 |
124
|
expimpd |
|
126 |
125
|
exlimdv |
|
127 |
29 126
|
syl5bi |
|
128 |
127
|
ralrimiv |
|
129 |
7
|
fmpttd |
|
130 |
129
|
ffnd |
|
131 |
|
eqid |
|
132 |
131
|
ptval |
|
133 |
2 130 132
|
syl2anc |
|
134 |
1 133
|
syl5eq |
|
135 |
134
|
adantr |
|
136 |
3
|
ralrimiva |
|
137 |
1
|
pttopon |
|
138 |
2 136 137
|
syl2anc |
|
139 |
|
toponuni |
|
140 |
138 139
|
syl |
|
141 |
140
|
adantr |
|
142 |
131
|
ptbas |
|
143 |
2 129 142
|
syl2anc |
|
144 |
143
|
adantr |
|
145 |
4
|
ralrimiva |
|
146 |
|
ss2ixp |
|
147 |
145 146
|
syl |
|
148 |
147
|
adantr |
|
149 |
11
|
clsss3 |
|
150 |
7 10 149
|
syl2anc |
|
151 |
150 9
|
sseqtrrd |
|
152 |
151
|
ralrimiva |
|
153 |
|
ss2ixp |
|
154 |
152 153
|
syl |
|
155 |
154
|
sselda |
|
156 |
135 141 144 148 155
|
elcls3 |
|
157 |
128 156
|
mpbird |
|
158 |
24 157
|
eqelssd |
|