Step |
Hyp |
Ref |
Expression |
1 |
|
2ndcsep.1 |
|
2 |
|
is2ndc |
|
3 |
|
vex |
|
4 |
|
difss |
|
5 |
|
ssdomg |
|
6 |
3 4 5
|
mp2 |
|
7 |
|
simpr |
|
8 |
|
domtr |
|
9 |
6 7 8
|
sylancr |
|
10 |
|
eldifsn |
|
11 |
|
n0 |
|
12 |
|
elunii |
|
13 |
|
simpl |
|
14 |
12 13
|
jca |
|
15 |
14
|
expcom |
|
16 |
15
|
eximdv |
|
17 |
16
|
imp |
|
18 |
|
df-rex |
|
19 |
17 18
|
sylibr |
|
20 |
11 19
|
sylan2b |
|
21 |
10 20
|
sylbi |
|
22 |
21
|
rgen |
|
23 |
|
vuniex |
|
24 |
|
eleq1 |
|
25 |
23 24
|
axcc4dom |
|
26 |
9 22 25
|
sylancl |
|
27 |
|
frn |
|
28 |
27
|
ad2antrl |
|
29 |
|
vex |
|
30 |
29
|
rnex |
|
31 |
30
|
elpw |
|
32 |
28 31
|
sylibr |
|
33 |
|
omelon |
|
34 |
7
|
adantr |
|
35 |
|
ondomen |
|
36 |
33 34 35
|
sylancr |
|
37 |
|
ssnum |
|
38 |
36 4 37
|
sylancl |
|
39 |
|
ffn |
|
40 |
39
|
ad2antrl |
|
41 |
|
dffn4 |
|
42 |
40 41
|
sylib |
|
43 |
|
fodomnum |
|
44 |
38 42 43
|
sylc |
|
45 |
9
|
adantr |
|
46 |
|
domtr |
|
47 |
44 45 46
|
syl2anc |
|
48 |
|
tgcl |
|
49 |
48
|
ad2antrr |
|
50 |
|
unitg |
|
51 |
50
|
elv |
|
52 |
51
|
eqcomi |
|
53 |
52
|
clsss3 |
|
54 |
49 28 53
|
syl2anc |
|
55 |
|
ne0i |
|
56 |
55
|
anim2i |
|
57 |
56 10
|
sylibr |
|
58 |
|
fnfvelrn |
|
59 |
39 58
|
sylan |
|
60 |
|
inelcm |
|
61 |
60
|
expcom |
|
62 |
59 61
|
syl |
|
63 |
62
|
ex |
|
64 |
63
|
a2d |
|
65 |
57 64
|
syl7 |
|
66 |
65
|
exp4a |
|
67 |
66
|
ralimdv2 |
|
68 |
67
|
imp |
|
69 |
68
|
ad2antlr |
|
70 |
|
eqidd |
|
71 |
52
|
a1i |
|
72 |
|
simplll |
|
73 |
28
|
adantr |
|
74 |
|
simpr |
|
75 |
70 71 72 73 74
|
elcls3 |
|
76 |
69 75
|
mpbird |
|
77 |
54 76
|
eqelssd |
|
78 |
|
breq1 |
|
79 |
|
fveqeq2 |
|
80 |
78 79
|
anbi12d |
|
81 |
80
|
rspcev |
|
82 |
32 47 77 81
|
syl12anc |
|
83 |
26 82
|
exlimddv |
|
84 |
|
unieq |
|
85 |
84 52 1
|
3eqtr4g |
|
86 |
85
|
pweqd |
|
87 |
|
fveq2 |
|
88 |
87
|
fveq1d |
|
89 |
88 85
|
eqeq12d |
|
90 |
89
|
anbi2d |
|
91 |
86 90
|
rexeqbidv |
|
92 |
83 91
|
syl5ibcom |
|
93 |
92
|
impr |
|
94 |
93
|
rexlimiva |
|
95 |
2 94
|
sylbi |
|