Step |
Hyp |
Ref |
Expression |
1 |
|
tsksdom |
|
2 |
|
cardidg |
|
3 |
2
|
ensymd |
|
4 |
3
|
adantr |
|
5 |
|
sdomentr |
|
6 |
1 4 5
|
syl2anc |
|
7 |
|
eqid |
|
8 |
7
|
rnmpt |
|
9 |
|
cardon |
|
10 |
|
sdomdom |
|
11 |
|
ondomen |
|
12 |
9 10 11
|
sylancr |
|
13 |
12
|
adantl |
|
14 |
|
vex |
|
15 |
14
|
imaex |
|
16 |
15 7
|
fnmpti |
|
17 |
|
dffn4 |
|
18 |
16 17
|
mpbi |
|
19 |
|
fodomnum |
|
20 |
13 18 19
|
mpisyl |
|
21 |
8 20
|
eqbrtrrid |
|
22 |
|
domsdomtr |
|
23 |
21 22
|
sylancom |
|
24 |
23
|
adantll |
|
25 |
6 24
|
mpdan |
|
26 |
|
ne0i |
|
27 |
|
tskcard |
|
28 |
26 27
|
sylan2 |
|
29 |
|
elina |
|
30 |
29
|
simp2bi |
|
31 |
28 30
|
syl |
|
32 |
25 31
|
breqtrrd |
|
33 |
32
|
3adant2 |
|
34 |
33
|
adantr |
|
35 |
28
|
3adant2 |
|
36 |
35
|
adantr |
|
37 |
|
inawina |
|
38 |
|
winalim |
|
39 |
36 37 38
|
3syl |
|
40 |
|
vex |
|
41 |
|
eqeq1 |
|
42 |
41
|
rexbidv |
|
43 |
40 42
|
elab |
|
44 |
|
imassrn |
|
45 |
|
f1ofo |
|
46 |
|
forn |
|
47 |
45 46
|
syl |
|
48 |
44 47
|
sseqtrid |
|
49 |
48
|
ad2antlr |
|
50 |
|
f1of1 |
|
51 |
|
elssuni |
|
52 |
|
vex |
|
53 |
52
|
f1imaen |
|
54 |
50 51 53
|
syl2an |
|
55 |
54
|
adantll |
|
56 |
|
simpl1 |
|
57 |
|
trss |
|
58 |
57
|
imp |
|
59 |
58
|
3adant1 |
|
60 |
59
|
sselda |
|
61 |
|
tsksdom |
|
62 |
56 60 61
|
syl2anc |
|
63 |
56 3
|
syl |
|
64 |
|
sdomentr |
|
65 |
62 63 64
|
syl2anc |
|
66 |
65
|
adantlr |
|
67 |
|
ensdomtr |
|
68 |
55 66 67
|
syl2anc |
|
69 |
36 30
|
syl |
|
70 |
69
|
adantr |
|
71 |
68 70
|
breqtrrd |
|
72 |
|
sseq1 |
|
73 |
|
breq1 |
|
74 |
72 73
|
anbi12d |
|
75 |
74
|
biimprcd |
|
76 |
49 71 75
|
syl2anc |
|
77 |
76
|
rexlimdva |
|
78 |
43 77
|
syl5bi |
|
79 |
78
|
ralrimiv |
|
80 |
|
fvex |
|
81 |
80
|
cfslb2n |
|
82 |
39 79 81
|
syl2anc |
|
83 |
34 82
|
mpd |
|
84 |
15
|
dfiun2 |
|
85 |
48
|
ralrimivw |
|
86 |
|
iunss |
|
87 |
85 86
|
sylibr |
|
88 |
|
fof |
|
89 |
|
foelrn |
|
90 |
89
|
ex |
|
91 |
|
eluni2 |
|
92 |
|
nfv |
|
93 |
|
nfiu1 |
|
94 |
93
|
nfel2 |
|
95 |
|
ssiun2 |
|
96 |
95
|
3ad2ant2 |
|
97 |
|
ffn |
|
98 |
97
|
3ad2ant1 |
|
99 |
51
|
3ad2ant2 |
|
100 |
|
simp3 |
|
101 |
|
fnfvima |
|
102 |
98 99 100 101
|
syl3anc |
|
103 |
96 102
|
sseldd |
|
104 |
103
|
3exp |
|
105 |
92 94 104
|
rexlimd |
|
106 |
91 105
|
syl5bi |
|
107 |
|
eleq1a |
|
108 |
106 107
|
syl6 |
|
109 |
108
|
rexlimdv |
|
110 |
88 90 109
|
sylsyld |
|
111 |
45 110
|
syl |
|
112 |
111
|
ssrdv |
|
113 |
87 112
|
eqssd |
|
114 |
84 113
|
eqtr3id |
|
115 |
114
|
necon3ai |
|
116 |
83 115
|
syl |
|
117 |
116
|
pm2.01da |
|
118 |
117
|
nexdv |
|
119 |
|
entr |
|
120 |
3 119
|
sylan2 |
|
121 |
|
bren |
|
122 |
120 121
|
sylib |
|
123 |
122
|
expcom |
|
124 |
123
|
3ad2ant1 |
|
125 |
118 124
|
mtod |
|
126 |
|
uniss |
|
127 |
|
df-tr |
|
128 |
127
|
biimpi |
|
129 |
126 128
|
sylan9ss |
|
130 |
129
|
expcom |
|
131 |
57 130
|
syld |
|
132 |
131
|
imp |
|
133 |
|
tsken |
|
134 |
132 133
|
sylan2 |
|
135 |
134
|
3impb |
|
136 |
135
|
ord |
|
137 |
125 136
|
mpd |
|