Step |
Hyp |
Ref |
Expression |
1 |
|
winacard |
|
2 |
|
winainf |
|
3 |
|
cardalephex |
|
4 |
2 3
|
syl |
|
5 |
1 4
|
mpbid |
|
6 |
5
|
adantr |
|
7 |
|
df-rex |
|
8 |
|
simprr |
|
9 |
8
|
eqcomd |
|
10 |
|
simprl |
|
11 |
|
onzsl |
|
12 |
10 11
|
sylib |
|
13 |
|
simplr |
|
14 |
|
fveq2 |
|
15 |
|
aleph0 |
|
16 |
14 15
|
eqtrdi |
|
17 |
|
eqtr |
|
18 |
16 17
|
sylan2 |
|
19 |
18
|
ex |
|
20 |
19
|
necon3ad |
|
21 |
8 13 20
|
sylc |
|
22 |
21
|
pm2.21d |
|
23 |
|
breq1 |
|
24 |
23
|
rexbidv |
|
25 |
|
elwina |
|
26 |
25
|
simp3bi |
|
27 |
26
|
ad3antrrr |
|
28 |
|
suceloni |
|
29 |
|
vex |
|
30 |
29
|
sucid |
|
31 |
|
alephord2i |
|
32 |
28 30 31
|
mpisyl |
|
33 |
32
|
ad2antrl |
|
34 |
|
simplrr |
|
35 |
|
fveq2 |
|
36 |
35
|
ad2antll |
|
37 |
34 36
|
eqtrd |
|
38 |
33 37
|
eleqtrrd |
|
39 |
24 27 38
|
rspcdva |
|
40 |
39
|
expr |
|
41 |
|
iscard |
|
42 |
41
|
simprbi |
|
43 |
|
rsp |
|
44 |
1 42 43
|
3syl |
|
45 |
44
|
ad3antrrr |
|
46 |
37
|
breq2d |
|
47 |
45 46
|
sylibd |
|
48 |
|
alephnbtwn2 |
|
49 |
|
pm3.21 |
|
50 |
48 49
|
mtoi |
|
51 |
47 50
|
syl6 |
|
52 |
51
|
imp |
|
53 |
52
|
nrexdv |
|
54 |
53
|
expr |
|
55 |
40 54
|
pm2.65d |
|
56 |
55
|
nrexdv |
|
57 |
56
|
pm2.21d |
|
58 |
|
simpr |
|
59 |
58
|
a1i |
|
60 |
22 57 59
|
3jaod |
|
61 |
12 60
|
mpd |
|
62 |
9 61
|
jca |
|
63 |
62
|
ex |
|
64 |
63
|
eximdv |
|
65 |
7 64
|
syl5bi |
|
66 |
6 65
|
mpd |
|