Step |
Hyp |
Ref |
Expression |
1 |
|
iunconn.2 |
|
2 |
|
iunconn.3 |
|
3 |
|
iunconn.4 |
|
4 |
|
iunconn.5 |
|
5 |
|
simpr |
|
6 |
|
simplr1 |
|
7 |
|
n0 |
|
8 |
|
elinel2 |
|
9 |
|
eliun |
|
10 |
|
rexn0 |
|
11 |
9 10
|
sylbi |
|
12 |
8 11
|
syl |
|
13 |
12
|
exlimiv |
|
14 |
7 13
|
sylbi |
|
15 |
6 14
|
syl |
|
16 |
|
simplll |
|
17 |
3
|
ralrimiva |
|
18 |
16 17
|
syl |
|
19 |
|
r19.2z |
|
20 |
15 18 19
|
syl2anc |
|
21 |
|
eliun |
|
22 |
20 21
|
sylibr |
|
23 |
5 22
|
sseldd |
|
24 |
|
elun |
|
25 |
23 24
|
sylib |
|
26 |
16 1
|
syl |
|
27 |
16 2
|
sylan |
|
28 |
16 3
|
sylan |
|
29 |
16 4
|
sylan |
|
30 |
|
simpllr |
|
31 |
30
|
simpld |
|
32 |
30
|
simprd |
|
33 |
|
simplr2 |
|
34 |
|
simplr3 |
|
35 |
|
nfv |
|
36 |
|
nfcv |
|
37 |
|
nfiu1 |
|
38 |
36 37
|
nfin |
|
39 |
|
nfcv |
|
40 |
38 39
|
nfne |
|
41 |
|
nfcv |
|
42 |
41 37
|
nfin |
|
43 |
42 39
|
nfne |
|
44 |
|
nfcv |
|
45 |
|
nfcv |
|
46 |
45 37
|
nfdif |
|
47 |
44 46
|
nfss |
|
48 |
40 43 47
|
nf3an |
|
49 |
35 48
|
nfan |
|
50 |
36 41
|
nfun |
|
51 |
37 50
|
nfss |
|
52 |
49 51
|
nfan |
|
53 |
26 27 28 29 31 32 33 34 5 52
|
iunconnlem |
|
54 |
|
incom |
|
55 |
54 34
|
eqsstrid |
|
56 |
|
uncom |
|
57 |
5 56
|
sseqtrdi |
|
58 |
26 27 28 29 32 31 6 55 57 52
|
iunconnlem |
|
59 |
|
ioran |
|
60 |
53 58 59
|
sylanbrc |
|
61 |
25 60
|
pm2.65da |
|
62 |
61
|
ex |
|
63 |
62
|
ralrimivva |
|
64 |
2
|
ralrimiva |
|
65 |
|
iunss |
|
66 |
64 65
|
sylibr |
|
67 |
|
connsub |
|
68 |
1 66 67
|
syl2anc |
|
69 |
63 68
|
mpbird |
|