Step |
Hyp |
Ref |
Expression |
1 |
|
iunconn.2 |
|
2 |
|
iunconn.3 |
|
3 |
|
iunconn.4 |
|
4 |
|
iunconn.5 |
|
5 |
|
iunconn.6 |
|
6 |
|
iunconn.7 |
|
7 |
|
iunconn.8 |
|
8 |
|
iunconn.9 |
|
9 |
|
iunconn.10 |
|
10 |
|
iunconn.11 |
|
11 |
|
n0 |
|
12 |
7 11
|
sylib |
|
13 |
|
elin |
|
14 |
|
eliun |
|
15 |
|
nfv |
|
16 |
10 15
|
nfan |
|
17 |
|
nfv |
|
18 |
4
|
adantr |
|
19 |
1
|
ad2antrr |
|
20 |
2
|
adantr |
|
21 |
5
|
ad2antrr |
|
22 |
6
|
ad2antrr |
|
23 |
|
simprr |
|
24 |
3
|
adantr |
|
25 |
|
inelcm |
|
26 |
23 24 25
|
syl2anc |
|
27 |
|
inelcm |
|
28 |
27
|
ad2antrl |
|
29 |
8
|
ad2antrr |
|
30 |
|
ssiun2 |
|
31 |
30
|
ad2antlr |
|
32 |
31
|
sscond |
|
33 |
29 32
|
sstrd |
|
34 |
|
inss1 |
|
35 |
|
toponss |
|
36 |
19 21 35
|
syl2anc |
|
37 |
34 36
|
sstrid |
|
38 |
|
reldisj |
|
39 |
37 38
|
syl |
|
40 |
33 39
|
mpbird |
|
41 |
9
|
ad2antrr |
|
42 |
31 41
|
sstrd |
|
43 |
19 20 21 22 26 28 40 42
|
nconnsubb |
|
44 |
43
|
expr |
|
45 |
18 44
|
mt2d |
|
46 |
45
|
an4s |
|
47 |
46
|
exp32 |
|
48 |
16 17 47
|
rexlimd |
|
49 |
14 48
|
syl5bi |
|
50 |
49
|
expimpd |
|
51 |
13 50
|
syl5bi |
|
52 |
51
|
exlimdv |
|
53 |
12 52
|
mpd |
|