Step |
Hyp |
Ref |
Expression |
1 |
|
cflim2.1 |
|
2 |
|
rabid |
|
3 |
|
velpw |
|
4 |
|
limord |
|
5 |
|
ordsson |
|
6 |
|
sstr |
|
7 |
6
|
expcom |
|
8 |
4 5 7
|
3syl |
|
9 |
8
|
imp |
|
10 |
9
|
3adant3 |
|
11 |
|
ssel2 |
|
12 |
|
eloni |
|
13 |
|
ordirr |
|
14 |
11 12 13
|
3syl |
|
15 |
|
ssel |
|
16 |
15
|
com12 |
|
17 |
16
|
adantl |
|
18 |
14 17
|
mtod |
|
19 |
10 18
|
sylan |
|
20 |
|
simpl2 |
|
21 |
|
sstr |
|
22 |
20 21
|
sylan |
|
23 |
19 22
|
mtand |
|
24 |
|
simpl3 |
|
25 |
24
|
sseq1d |
|
26 |
23 25
|
mtbird |
|
27 |
|
unissb |
|
28 |
26 27
|
sylnib |
|
29 |
28
|
nrexdv |
|
30 |
|
ssel |
|
31 |
|
ssel |
|
32 |
|
ontri1 |
|
33 |
32
|
ancoms |
|
34 |
|
vex |
|
35 |
|
vex |
|
36 |
34 35
|
brcnv |
|
37 |
|
epel |
|
38 |
36 37
|
bitri |
|
39 |
38
|
notbii |
|
40 |
33 39
|
bitr4di |
|
41 |
40
|
a1i |
|
42 |
30 31 41
|
syl2and |
|
43 |
42
|
impl |
|
44 |
43
|
ralbidva |
|
45 |
44
|
rexbidva |
|
46 |
10 45
|
syl |
|
47 |
29 46
|
mtbid |
|
48 |
|
vex |
|
49 |
48
|
a1i |
|
50 |
|
epweon |
|
51 |
|
wess |
|
52 |
50 51
|
mpi |
|
53 |
|
weso |
|
54 |
52 53
|
syl |
|
55 |
|
cnvso |
|
56 |
54 55
|
sylib |
|
57 |
|
onssnum |
|
58 |
48 57
|
mpan |
|
59 |
|
cardid2 |
|
60 |
|
ensym |
|
61 |
58 59 60
|
3syl |
|
62 |
|
nnsdom |
|
63 |
|
ensdomtr |
|
64 |
61 62 63
|
syl2an |
|
65 |
|
isfinite |
|
66 |
64 65
|
sylibr |
|
67 |
|
wofi |
|
68 |
56 66 67
|
syl2an2r |
|
69 |
10 68
|
sylan |
|
70 |
|
wefr |
|
71 |
69 70
|
syl |
|
72 |
|
ssidd |
|
73 |
|
unieq |
|
74 |
|
uni0 |
|
75 |
73 74
|
eqtrdi |
|
76 |
|
eqeq1 |
|
77 |
75 76
|
syl5ib |
|
78 |
|
nlim0 |
|
79 |
|
limeq |
|
80 |
78 79
|
mtbiri |
|
81 |
77 80
|
syl6 |
|
82 |
81
|
necon2ad |
|
83 |
82
|
impcom |
|
84 |
83
|
3adant2 |
|
85 |
84
|
adantr |
|
86 |
|
fri |
|
87 |
49 71 72 85 86
|
syl22anc |
|
88 |
47 87
|
mtand |
|
89 |
|
cardon |
|
90 |
|
eloni |
|
91 |
|
ordom |
|
92 |
|
ordtri1 |
|
93 |
91 92
|
mpan |
|
94 |
89 90 93
|
mp2b |
|
95 |
88 94
|
sylibr |
|
96 |
3 95
|
syl3an2b |
|
97 |
96
|
3expb |
|
98 |
2 97
|
sylan2b |
|
99 |
98
|
ralrimiva |
|
100 |
|
ssiin |
|
101 |
99 100
|
sylibr |
|
102 |
1
|
cflim3 |
|
103 |
101 102
|
sseqtrrd |
|
104 |
|
fvex |
|
105 |
104
|
dfiin2 |
|
106 |
102 105
|
eqtrdi |
|
107 |
|
cardlim |
|
108 |
|
sseq2 |
|
109 |
|
limeq |
|
110 |
108 109
|
bibi12d |
|
111 |
107 110
|
mpbiri |
|
112 |
111
|
rexlimivw |
|
113 |
112
|
ss2abi |
|
114 |
|
eleq1 |
|
115 |
89 114
|
mpbiri |
|
116 |
115
|
rexlimivw |
|
117 |
116
|
abssi |
|
118 |
|
fvex |
|
119 |
106 118
|
eqeltrrdi |
|
120 |
|
intex |
|
121 |
119 120
|
sylibr |
|
122 |
|
onint |
|
123 |
117 121 122
|
sylancr |
|
124 |
113 123
|
sseldi |
|
125 |
106 124
|
eqeltrd |
|
126 |
|
sseq2 |
|
127 |
|
limeq |
|
128 |
126 127
|
bibi12d |
|
129 |
118 128
|
elab |
|
130 |
125 129
|
sylib |
|
131 |
103 130
|
mpbid |
|
132 |
|
eloni |
|
133 |
|
ordzsl |
|
134 |
132 133
|
sylib |
|
135 |
|
df-3or |
|
136 |
|
orcom |
|
137 |
|
df-or |
|
138 |
135 136 137
|
3bitri |
|
139 |
134 138
|
sylib |
|
140 |
|
fveq2 |
|
141 |
|
cf0 |
|
142 |
140 141
|
eqtrdi |
|
143 |
|
limeq |
|
144 |
142 143
|
syl |
|
145 |
78 144
|
mtbiri |
|
146 |
|
1n0 |
|
147 |
|
df1o2 |
|
148 |
147
|
unieqi |
|
149 |
|
0ex |
|
150 |
149
|
unisn |
|
151 |
148 150
|
eqtri |
|
152 |
146 151
|
neeqtrri |
|
153 |
|
limuni |
|
154 |
153
|
necon3ai |
|
155 |
152 154
|
ax-mp |
|
156 |
|
fveq2 |
|
157 |
|
cfsuc |
|
158 |
156 157
|
sylan9eqr |
|
159 |
|
limeq |
|
160 |
158 159
|
syl |
|
161 |
155 160
|
mtbiri |
|
162 |
161
|
rexlimiva |
|
163 |
145 162
|
jaoi |
|
164 |
139 163
|
syl6 |
|
165 |
164
|
con4d |
|
166 |
|
cff |
|
167 |
166
|
fdmi |
|
168 |
167
|
eleq2i |
|
169 |
|
ndmfv |
|
170 |
168 169
|
sylnbir |
|
171 |
170 143
|
syl |
|
172 |
78 171
|
mtbiri |
|
173 |
172
|
pm2.21d |
|
174 |
165 173
|
pm2.61i |
|
175 |
131 174
|
impbii |
|