Step |
Hyp |
Ref |
Expression |
1 |
|
ttukeylem.1 |
|
2 |
|
ttukeylem.2 |
|
3 |
|
ttukeylem.3 |
|
4 |
|
ttukeylem.4 |
|
5 |
|
cardon |
|
6 |
5
|
onsuci |
|
7 |
6
|
a1i |
|
8 |
|
onelon |
|
9 |
7 8
|
sylan |
|
10 |
|
eleq1 |
|
11 |
|
fveq2 |
|
12 |
11
|
eleq1d |
|
13 |
10 12
|
imbi12d |
|
14 |
13
|
imbi2d |
|
15 |
|
eleq1 |
|
16 |
|
fveq2 |
|
17 |
16
|
eleq1d |
|
18 |
15 17
|
imbi12d |
|
19 |
18
|
imbi2d |
|
20 |
|
r19.21v |
|
21 |
6
|
onordi |
|
22 |
21
|
a1i |
|
23 |
|
ordelss |
|
24 |
22 23
|
sylan |
|
25 |
24
|
sselda |
|
26 |
|
biimt |
|
27 |
25 26
|
syl |
|
28 |
27
|
ralbidva |
|
29 |
6
|
onssi |
|
30 |
|
simprl |
|
31 |
29 30
|
sseldi |
|
32 |
1 2 3 4
|
ttukeylem3 |
|
33 |
31 32
|
syldan |
|
34 |
2
|
ad3antrrr |
|
35 |
|
simpr |
|
36 |
35
|
elin2d |
|
37 |
35
|
elin1d |
|
38 |
37
|
elpwid |
|
39 |
4
|
tfr1 |
|
40 |
|
fnfun |
|
41 |
|
funiunfv |
|
42 |
39 40 41
|
mp2b |
|
43 |
38 42
|
sseqtrrdi |
|
44 |
|
dfss3 |
|
45 |
|
eliun |
|
46 |
45
|
ralbii |
|
47 |
44 46
|
bitri |
|
48 |
43 47
|
sylib |
|
49 |
|
fveq2 |
|
50 |
49
|
eleq2d |
|
51 |
50
|
ac6sfi |
|
52 |
36 48 51
|
syl2anc |
|
53 |
|
eleq1 |
|
54 |
|
simp-4l |
|
55 |
|
fveq2 |
|
56 |
55
|
eleq1d |
|
57 |
|
simplrr |
|
58 |
57
|
ad2antrr |
|
59 |
|
simprrl |
|
60 |
59
|
adantr |
|
61 |
|
frn |
|
62 |
60 61
|
syl |
|
63 |
31
|
ad3antrrr |
|
64 |
|
onss |
|
65 |
63 64
|
syl |
|
66 |
62 65
|
sstrd |
|
67 |
36
|
adantrr |
|
68 |
67
|
adantr |
|
69 |
|
ffn |
|
70 |
60 69
|
syl |
|
71 |
|
dffn4 |
|
72 |
70 71
|
sylib |
|
73 |
|
fofi |
|
74 |
68 72 73
|
syl2anc |
|
75 |
|
dm0rn0 |
|
76 |
59
|
fdmd |
|
77 |
76
|
eqeq1d |
|
78 |
75 77
|
bitr3id |
|
79 |
78
|
necon3bid |
|
80 |
79
|
biimpar |
|
81 |
|
ordunifi |
|
82 |
66 74 80 81
|
syl3anc |
|
83 |
62 82
|
sseldd |
|
84 |
56 58 83
|
rspcdva |
|
85 |
|
simp-4l |
|
86 |
31
|
ad3antrrr |
|
87 |
86 64
|
syl |
|
88 |
|
ffvelrn |
|
89 |
88
|
adantl |
|
90 |
87 89
|
sseldd |
|
91 |
61
|
ad2antrl |
|
92 |
91 87
|
sstrd |
|
93 |
|
vex |
|
94 |
93
|
rnex |
|
95 |
94
|
ssonunii |
|
96 |
92 95
|
syl |
|
97 |
69
|
ad2antrl |
|
98 |
|
simprr |
|
99 |
|
fnfvelrn |
|
100 |
97 98 99
|
syl2anc |
|
101 |
|
elssuni |
|
102 |
100 101
|
syl |
|
103 |
1 2 3 4
|
ttukeylem5 |
|
104 |
85 90 96 102 103
|
syl13anc |
|
105 |
104
|
sseld |
|
106 |
105
|
anassrs |
|
107 |
106
|
ralimdva |
|
108 |
107
|
expimpd |
|
109 |
108
|
impr |
|
110 |
109
|
adantr |
|
111 |
|
dfss3 |
|
112 |
110 111
|
sylibr |
|
113 |
1 2 3
|
ttukeylem2 |
|
114 |
54 84 112 113
|
syl12anc |
|
115 |
|
0ss |
|
116 |
1 2 3
|
ttukeylem2 |
|
117 |
115 116
|
mpanr2 |
|
118 |
2 117
|
mpdan |
|
119 |
118
|
ad3antrrr |
|
120 |
53 114 119
|
pm2.61ne |
|
121 |
120
|
expr |
|
122 |
121
|
exlimdv |
|
123 |
52 122
|
mpd |
|
124 |
123
|
ex |
|
125 |
124
|
ssrdv |
|
126 |
1 2 3
|
ttukeylem1 |
|
127 |
126
|
ad2antrr |
|
128 |
125 127
|
mpbird |
|
129 |
128
|
adantr |
|
130 |
34 129
|
ifclda |
|
131 |
|
uneq2 |
|
132 |
131
|
eleq1d |
|
133 |
|
un0 |
|
134 |
|
uneq2 |
|
135 |
133 134
|
syl5eqr |
|
136 |
135
|
eleq1d |
|
137 |
|
simpr |
|
138 |
|
fveq2 |
|
139 |
138
|
eleq1d |
|
140 |
|
simplrr |
|
141 |
|
vuniex |
|
142 |
141
|
sucid |
|
143 |
|
eloni |
|
144 |
|
orduniorsuc |
|
145 |
31 143 144
|
3syl |
|
146 |
145
|
orcanai |
|
147 |
142 146
|
eleqtrrid |
|
148 |
139 140 147
|
rspcdva |
|
149 |
148
|
adantr |
|
150 |
132 136 137 149
|
ifbothda |
|
151 |
130 150
|
ifclda |
|
152 |
33 151
|
eqeltrd |
|
153 |
152
|
expr |
|
154 |
28 153
|
sylbird |
|
155 |
154
|
ex |
|
156 |
155
|
com23 |
|
157 |
156
|
a2i |
|
158 |
20 157
|
sylbi |
|
159 |
158
|
a1i |
|
160 |
14 19 159
|
tfis3 |
|
161 |
160
|
impd |
|
162 |
9 161
|
mpcom |
|