Step |
Hyp |
Ref |
Expression |
1 |
|
cmetcau.1 |
|
2 |
|
cmetcau.3 |
|
3 |
|
cmetcau.4 |
|
4 |
|
cmetcau.5 |
|
5 |
|
cmetcau.6 |
|
6 |
|
cmetmet |
|
7 |
2 6
|
syl |
|
8 |
|
metxmet |
|
9 |
7 8
|
syl |
|
10 |
1
|
mopntopon |
|
11 |
9 10
|
syl |
|
12 |
|
1z |
|
13 |
|
nnuz |
|
14 |
13
|
uzfbas |
|
15 |
12 14
|
mp1i |
|
16 |
|
fgcl |
|
17 |
15 16
|
syl |
|
18 |
|
elfvdm |
|
19 |
2 18
|
syl |
|
20 |
|
cnex |
|
21 |
20
|
a1i |
|
22 |
|
caufpm |
|
23 |
9 4 22
|
syl2anc |
|
24 |
|
elpm2g |
|
25 |
24
|
simprbda |
|
26 |
19 21 23 25
|
syl21anc |
|
27 |
26
|
adantr |
|
28 |
27
|
ffvelrnda |
|
29 |
3
|
ad2antrr |
|
30 |
28 29
|
ifclda |
|
31 |
30 5
|
fmptd |
|
32 |
|
flfval |
|
33 |
11 17 31 32
|
syl3anc |
|
34 |
|
eqid |
|
35 |
34
|
fmfg |
|
36 |
19 15 31 35
|
syl3anc |
|
37 |
36
|
oveq2d |
|
38 |
33 37
|
eqtr4d |
|
39 |
|
biidd |
|
40 |
|
1zzd |
|
41 |
13 9 40
|
iscau3 |
|
42 |
41
|
simplbda |
|
43 |
4 42
|
mpdan |
|
44 |
|
simp1 |
|
45 |
44
|
ralimi |
|
46 |
45
|
reximi |
|
47 |
46
|
ralimi |
|
48 |
43 47
|
syl |
|
49 |
|
1rp |
|
50 |
49
|
a1i |
|
51 |
39 48 50
|
rspcdva |
|
52 |
|
dfss3 |
|
53 |
|
nnsscn |
|
54 |
31 53
|
jctir |
|
55 |
|
elpm2r |
|
56 |
19 21 54 55
|
syl21anc |
|
57 |
56
|
adantr |
|
58 |
|
eqid |
|
59 |
9
|
adantr |
|
60 |
|
nnz |
|
61 |
60
|
ad2antrl |
|
62 |
|
eqidd |
|
63 |
|
eqidd |
|
64 |
58 59 61 62 63
|
iscau4 |
|
65 |
64
|
simplbda |
|
66 |
4 65
|
mpidan |
|
67 |
|
simprl |
|
68 |
|
eluznn |
|
69 |
67 68
|
sylan |
|
70 |
|
eluznn |
|
71 |
5 30
|
dmmptd |
|
72 |
71
|
adantr |
|
73 |
72
|
eleq2d |
|
74 |
73
|
biimpar |
|
75 |
74
|
a1d |
|
76 |
|
idd |
|
77 |
|
idd |
|
78 |
75 76 77
|
3anim123d |
|
79 |
70 78
|
sylan2 |
|
80 |
79
|
anassrs |
|
81 |
80
|
ralimdva |
|
82 |
69 81
|
syldan |
|
83 |
82
|
reximdva |
|
84 |
83
|
ralimdv |
|
85 |
66 84
|
mpd |
|
86 |
|
eluznn |
|
87 |
67 86
|
sylan |
|
88 |
|
simprr |
|
89 |
88
|
sselda |
|
90 |
|
iftrue |
|
91 |
90
|
adantl |
|
92 |
|
fvex |
|
93 |
91 92
|
eqeltrdi |
|
94 |
|
eleq1w |
|
95 |
|
fveq2 |
|
96 |
94 95
|
ifbieq1d |
|
97 |
96 5
|
fvmptg |
|
98 |
93 97
|
syldan |
|
99 |
98 91
|
eqtrd |
|
100 |
87 89 99
|
syl2anc |
|
101 |
88
|
sselda |
|
102 |
69 101
|
elind |
|
103 |
|
fveq2 |
|
104 |
|
fveq2 |
|
105 |
103 104
|
eqeq12d |
|
106 |
|
elin |
|
107 |
106 99
|
sylbi |
|
108 |
105 107
|
vtoclga |
|
109 |
102 108
|
syl |
|
110 |
58 59 61 100 109
|
iscau4 |
|
111 |
57 85 110
|
mpbir2and |
|
112 |
111
|
expr |
|
113 |
52 112
|
syl5bir |
|
114 |
113
|
rexlimdva |
|
115 |
51 114
|
mpd |
|
116 |
|
eqid |
|
117 |
13 116
|
caucfil |
|
118 |
9 40 31 117
|
syl3anc |
|
119 |
115 118
|
mpbid |
|
120 |
1
|
cmetcvg |
|
121 |
2 119 120
|
syl2anc |
|
122 |
38 121
|
eqnetrd |
|
123 |
|
n0 |
|
124 |
122 123
|
sylib |
|
125 |
13 34
|
lmflf |
|
126 |
11 40 31 125
|
syl3anc |
|
127 |
23
|
adantr |
|
128 |
|
lmcl |
|
129 |
11 128
|
sylan |
|
130 |
1 9 13 40
|
lmmbr3 |
|
131 |
130
|
biimpa |
|
132 |
131
|
simp3d |
|
133 |
|
r19.26 |
|
134 |
13
|
rexanuz2 |
|
135 |
|
simprl |
|
136 |
99
|
ad2ant2lr |
|
137 |
|
simprr2 |
|
138 |
136 137
|
eqeltrrd |
|
139 |
136
|
oveq1d |
|
140 |
|
simprr3 |
|
141 |
139 140
|
eqbrtrrd |
|
142 |
135 138 141
|
3jca |
|
143 |
142
|
ex |
|
144 |
86 143
|
sylan2 |
|
145 |
144
|
anassrs |
|
146 |
145
|
ralimdva |
|
147 |
146
|
reximdva |
|
148 |
134 147
|
syl5bir |
|
149 |
148
|
ralimdv |
|
150 |
133 149
|
syl5bir |
|
151 |
48 150
|
mpand |
|
152 |
151
|
adantr |
|
153 |
132 152
|
mpd |
|
154 |
9
|
adantr |
|
155 |
|
1zzd |
|
156 |
1 154 13 155
|
lmmbr3 |
|
157 |
127 129 153 156
|
mpbir3and |
|
158 |
|
lmrel |
|
159 |
158
|
releldmi |
|
160 |
157 159
|
syl |
|
161 |
160
|
ex |
|
162 |
126 161
|
sylbird |
|
163 |
162
|
exlimdv |
|
164 |
124 163
|
mpd |
|